MSC2020 database

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class="folderWrap4"> <div class="folderContent"> <form name="searchMSC2" method="get" action="msc2020.html" style="width: auto;"> <div class="summary" id="summary2"> </div> <br style="clear: both;" /> <div class="widgets"> <div class="controlsPosition2"> <h3>Browse Classification</h3> <span class="enter_msc" style="float:both;">Select a 2 digit classification</span><br /> <select name="t" id="selectTarget2" tabindex="1" onchange="if (this.value != '') { this.form.elements[2].click(); }"> <option value="">Select a Mathematics subject classification</option> <option value="00-XX">00 General and overarching topics; collections</option> <option value="01-XX">01 History and biography</option> <option value="03-XX">03 Mathematical logic and foundations</option> <option value="05-XX">05 Combinatorics </option> <option value="06-XX">06 Order, lattices, ordered algebraic structures</option> <option value="08-XX">08 General algebraic systems</option> <option value="11-XX">11 Number 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value="Search" class="button" /> </div> </div> </div> <input type="hidden" name="ls" value="Ct" /> <div class="resultSet" id="resultSet2"> <div class="buttonBox"> <input type="submit" name="btn" value="Clear" class="button" /> </div> <span class="legend"> < <a href="msc2020.html?t=34-XX&btn=Current">34-XX</a> | <a href="msc2020.html?t=&btn=Current">Up</a> | <a href="msc2020.html?t=37-XX&btn=Current">37-XX</a> > </span> <table class="results"> <tr class="current"> <td><a href="msc2020.html?t=35-XX&btn=Current" title=""><b>35-XX</b></a></td> <td></td> <td></td> <td><b>Partial differential equations</b></td> </tr> <tr class="current"> <td></td> <td></td> <td>35-00  </td> <td>General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to partial differential equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35-01  </td> <td>Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations</td> </tr> <tr class="current"> <td></td> <td></td> <td><span class="highlight">35-02</span>  </td> <td>Research exposition (monographs, survey articles) pertaining to partial differential equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35-03  </td> <td>History of partial differential equations [Consider also classification numbers from Section <a href="msc2020.html?t=01-XX&btn=Current">01-XX</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35-04  </td> <td>Software, source code, etc. for problems pertaining to partial differential equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35-06  </td> <td>Proceedings, conferences, collections, etc. pertaining to partial differential equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35-11  </td> <td>Research data for problems pertaining to partial differential equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A01  </td> <td>Existence problems for PDEs: global existence, local existence, non-existence</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A02  </td> <td>Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A08  </td> <td>Fundamental solutions to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A09  </td> <td>Classical solutions to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A10  </td> <td>Cauchy-Kovalevskaya theorems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A15  </td> <td>Variational methods applied to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A16  </td> <td>Topological and monotonicity methods applied to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A17  </td> <td>Parametrices in context of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A18  </td> <td>Wave front sets in context of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A20  </td> <td>Analyticity in context of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A21  </td> <td>Singularity in context of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A22  </td> <td>Transform methods (e.g., integral transforms) applied to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A23  </td> <td>Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A24  </td> <td>Methods of ordinary differential equations applied to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A25  </td> <td>Other special methods applied to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A27  </td> <td>Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs [See also <a href="msc2020.html?t=32C38&btn=Current">32C38</a>, <a href="msc2020.html?t=58J15&btn=Current">58J15</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A30  </td> <td>Geometric theory, characteristics, transformations in context of PDEs [See also <a href="msc2020.html?t=58J70&btn=Current">58J70</a>, <a href="msc2020.html?t=58J72&btn=Current">58J72</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A35  </td> <td>Theoretical approximation in context of PDEs {For numerical analysis, see <a href="msc2020.html?t=65Mxx&btn=Current">65Mxx</a>, <a href="msc2020.html?t=65Nxx&btn=Current">65Nxx</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35A99  </td> <td>None of the above, but in this section</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B05  </td> <td>Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B06  </td> <td>Symmetries, invariants, etc. in context of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B07  </td> <td>Axially symmetric solutions to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B08  </td> <td>Entire solutions to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B09  </td> <td>Positive solutions to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B10  </td> <td>Periodic solutions to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B15  </td> <td>Almost and pseudo-almost periodic solutions to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B20  </td> <td>Perturbations in context of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B25  </td> <td>Singular perturbations in context of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B27  </td> <td>Homogenization in context of PDEs; PDEs in media with periodic structure [See also <a href="msc2020.html?t=74Q05&btn=Current">74Q05</a>, <a href="msc2020.html?t=74Q10&btn=Current">74Q10</a>, <a href="msc2020.html?t=76M50&btn=Current">76M50</a>, <a href="msc2020.html?t=78M40&btn=Current">78M40</a>, <a href="msc2020.html?t=80M40&btn=Current">80M40</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B30  </td> <td>Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs [See also <a href="msc2020.html?t=37Cxx&btn=Current">37Cxx</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B32  </td> <td>Bifurcations in context of PDEs [See also <a href="msc2020.html?t=34C23&btn=Current">34C23</a>, <a href="msc2020.html?t=34F10&btn=Current">34F10</a>, <a href="msc2020.html?t=34H20&btn=Current">34H20</a>, <a href="msc2020.html?t=37F46&btn=Current">37F46</a>, <a href="msc2020.html?t=37Gxx&btn=Current">37Gxx</a>, <a href="msc2020.html?t=37H20&btn=Current">37H20</a>, <a href="msc2020.html?t=37J20&btn=Current">37J20</a>, <a href="msc2020.html?t=37K50&btn=Current">37K50</a>, <a href="msc2020.html?t=37L10&btn=Current">37L10</a>, <a href="msc2020.html?t=37M20&btn=Current">37M20</a>, <a href="msc2020.html?t=47J15&btn=Current">47J15</a>, <a href="msc2020.html?t=58E05&btn=Current">58E05</a>, <a href="msc2020.html?t=58E07&btn=Current">58E07</a>, <a href="msc2020.html?t=58J55&btn=Current">58J55</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B33  </td> <td>Critical exponents in context of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B34  </td> <td>Resonance in context of PDEs [See also <a href="msc2020.html?t=34F15&btn=Current">34F15</a>, <a href="msc2020.html?t=70J40&btn=Current">70J40</a>, <a href="msc2020.html?t=70K28&btn=Current">70K28</a>, <a href="msc2020.html?t=70K30&btn=Current">70K30</a>, <a href="msc2020.html?t=81U24&btn=Current">81U24</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B35  </td> <td>Stability in context of PDEs [See also <a href="msc2020.html?t=34Dxx&btn=Current">34Dxx</a>, <a href="msc2020.html?t=37B25&btn=Current">37B25</a>, <a href="msc2020.html?t=37C20&btn=Current">37C20</a>, <a href="msc2020.html?t=37C75&btn=Current">37C75</a>, <a href="msc2020.html?t=37F15&btn=Current">37F15</a>, <a href="msc2020.html?t=37J25&btn=Current">37J25</a>, <a href="msc2020.html?t=37K45&btn=Current">37K45</a>, <a href="msc2020.html?t=37L15&btn=Current">37L15</a>, <a href="msc2020.html?t=49K40&btn=Current">49K40</a>, <a href="msc2020.html?t=58K25&btn=Current">58K25</a>, <a href="msc2020.html?t=93Dxx&btn=Current">93Dxx</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B36  </td> <td>Pattern formations in context of PDEs [See also <a href="msc2020.html?t=92C15&btn=Current">92C15</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B38  </td> <td>Critical points of functionals in context of PDEs (e.g., energy functionals) [See also <a href="msc2020.html?t=57R70&btn=Current">57R70</a>, <a href="msc2020.html?t=58K05&btn=Current">58K05</a>, <a href="msc2020.html?t=58E05&btn=Current">58E05</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B40  </td> <td>Asymptotic behavior of solutions to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B41  </td> <td>Attractors [See also <a href="msc2020.html?t=34D45&btn=Current">34D45</a>, <a href="msc2020.html?t=37B35&btn=Current">37B35</a>, <a href="msc2020.html?t=37C70&btn=Current">37C70</a>, <a href="msc2020.html?t=37D45&btn=Current">37D45</a>, <a href="msc2020.html?t=37G35&btn=Current">37G35</a>, <a href="msc2020.html?t=37L30&btn=Current">37L30</a>, <a href="msc2020.html?t=37M22&btn=Current">37M22</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B42  </td> <td>Inertial manifolds [See also <a href="msc2020.html?t=37L25&btn=Current">37L25</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B44  </td> <td>Blow-up in context of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B45  </td> <td>A priori estimates in context of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B50  </td> <td>Maximum principles in context of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B51  </td> <td>Comparison principles in context of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B53  </td> <td>Liouville theorems and Phragm茅n-Lindel枚f theorems in context of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B60  </td> <td>Continuation and prolongation of solutions to PDEs [See also <a href="msc2020.html?t=58A15&btn=Current">58A15</a>, <a href="msc2020.html?t=58A17&btn=Current">58A17</a>, <a href="msc2020.html?t=58Hxx&btn=Current">58Hxx</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B65  </td> <td>Smoothness and regularity of solutions to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35B99  </td> <td>None of the above, but in this section</td> </tr> <tr class="current"> <td></td> <td></td> <td>35C05  </td> <td>Solutions to PDEs in closed form</td> </tr> <tr class="current"> <td></td> <td></td> <td>35C06  </td> <td>Self-similar solutions to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35C07  </td> <td>Traveling wave solutions</td> </tr> <tr class="current"> <td></td> <td></td> <td>35C08  </td> <td>Soliton solutions [See also <a href="msc2020.html?t=37K40&btn=Current">37K40</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35C09  </td> <td>Trigonometric solutions to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35C10  </td> <td>Series solutions to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35C11  </td> <td>Polynomial solutions to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35C15  </td> <td>Integral representations of solutions to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35C20  </td> <td>Asymptotic expansions of solutions to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35C99  </td> <td>None of the above, but in this section</td> </tr> <tr class="current"> <td></td> <td></td> <td>35D30  </td> <td>Weak solutions to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35D35  </td> <td>Strong solutions to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35D40  </td> <td>Viscosity solutions to PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35D99  </td> <td>None of the above, but in this section</td> </tr> <tr class="current"> <td></td> <td></td> <td>35E05  </td> <td>Fundamental solutions to PDEs and systems of PDEs with constant coefficients</td> </tr> <tr class="current"> <td></td> <td></td> <td>35E10  </td> <td>Convexity properties of solutions to PDEs with constant coefficients</td> </tr> <tr class="current"> <td></td> <td></td> <td>35E15  </td> <td>Initial value problems for PDEs and systems of PDEs with constant coefficients</td> </tr> <tr class="current"> <td></td> <td></td> <td>35E20  </td> <td>General theory of PDEs and systems of PDEs with constant coefficients</td> </tr> <tr class="current"> <td></td> <td></td> <td>35E99  </td> <td>None of the above, but in this section</td> </tr> <tr class="current"> <td></td> <td></td> <td>35F05  </td> <td>Linear first-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35F10  </td> <td>Initial value problems for linear first-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35F15  </td> <td>Boundary value problems for linear first-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35F16  </td> <td>Initial-boundary value problems for linear first-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35F20  </td> <td>Nonlinear first-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35F21  </td> <td>Hamilton-Jacobi equations {For calculus of variations and optimal control, see <a href="msc2020.html?t=49Lxx&btn=Current">49Lxx</a>; for mechanics of particles and systems, see <a href="msc2020.html?t=70H20&btn=Current">70H20</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35F25  </td> <td>Initial value problems for nonlinear first-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35F30  </td> <td>Boundary value problems for nonlinear first-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35F31  </td> <td>Initial-boundary value problems for nonlinear first-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35F35  </td> <td>Systems of linear first-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35F40  </td> <td>Initial value problems for systems of linear first-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35F45  </td> <td>Boundary value problems for systems of linear first-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35F46  </td> <td>Initial-boundary value problems for systems of linear first-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35F50  </td> <td>Systems of nonlinear first-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35F55  </td> <td>Initial value problems for systems of nonlinear first-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35F60  </td> <td>Boundary value problems for systems of nonlinear first-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35F61  </td> <td>Initial-boundary value problems for systems of nonlinear first-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35F99  </td> <td>None of the above, but in this section</td> </tr> <tr class="current"> <td></td> <td></td> <td>35G05  </td> <td>Linear higher-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35G10  </td> <td>Initial value problems for linear higher-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35G15  </td> <td>Boundary value problems for linear higher-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35G16  </td> <td>Initial-boundary value problems for linear higher-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35G20  </td> <td>Nonlinear higher-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35G25  </td> <td>Initial value problems for nonlinear higher-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35G30  </td> <td>Boundary value problems for nonlinear higher-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35G31  </td> <td>Initial-boundary value problems for nonlinear higher-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35G35  </td> <td>Systems of linear higher-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35G40  </td> <td>Initial value problems for systems of linear higher-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35G45  </td> <td>Boundary value problems for systems of linear higher-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35G46  </td> <td>Initial-boundary value problems for systems of linear higher-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35G50  </td> <td>Systems of nonlinear higher-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35G55  </td> <td>Initial value problems for systems of nonlinear higher-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35G60  </td> <td>Boundary value problems for systems of nonlinear higher-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35G61  </td> <td>Initial-boundary value problems for systems of nonlinear higher-order PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35G99  </td> <td>None of the above, but in this section</td> </tr> <tr class="current"> <td></td> <td></td> <td>35H10  </td> <td>Hypoelliptic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35H20  </td> <td>Subelliptic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35H30  </td> <td>Quasielliptic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35H99  </td> <td>None of the above, but in this section</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J05  </td> <td>Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation [See also <a href="msc2020.html?t=31Axx&btn=Current">31Axx</a>, <a href="msc2020.html?t=31Bxx&btn=Current">31Bxx</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J08  </td> <td>Green's functions for elliptic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J10  </td> <td>Schr枚dinger operator, Schr枚dinger equation {For ordinary differential equations, see <a href="msc2020.html?t=34L40&btn=Current">34L40</a>; for operator theory, see <a href="msc2020.html?t=47D08&btn=Current">47D08</a>; for quantum theory, see <a href="msc2020.html?t=81Q05&btn=Current">81Q05</a>; for statistical mechanics, see <a href="msc2020.html?t=82B44&btn=Current">82B44</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J15  </td> <td>Second-order elliptic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J20  </td> <td>Variational methods for second-order elliptic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J25  </td> <td>Boundary value problems for second-order elliptic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J30  </td> <td>Higher-order elliptic equations [See also <a href="msc2020.html?t=31A30&btn=Current">31A30</a>, <a href="msc2020.html?t=31B30&btn=Current">31B30</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J35  </td> <td>Variational methods for higher-order elliptic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J40  </td> <td>Boundary value problems for higher-order elliptic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J46  </td> <td>First-order elliptic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J47  </td> <td>Second-order elliptic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J48  </td> <td>Higher-order elliptic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J50  </td> <td>Variational methods for elliptic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J56  </td> <td>Boundary value problems for first-order elliptic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J57  </td> <td>Boundary value problems for second-order elliptic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J58  </td> <td>Boundary value problems for higher-order elliptic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J60  </td> <td>Nonlinear elliptic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J61  </td> <td>Semilinear elliptic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J62  </td> <td>Quasilinear elliptic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J65  </td> <td>Nonlinear boundary value problems for linear elliptic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J66  </td> <td>Nonlinear boundary value problems for nonlinear elliptic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J67  </td> <td>Boundary values of solutions to elliptic equations and elliptic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J70  </td> <td>Degenerate elliptic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J75  </td> <td>Singular elliptic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J86  </td> <td>Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators [See also <a href="msc2020.html?t=35R35&btn=Current">35R35</a>, <a href="msc2020.html?t=49J40&btn=Current">49J40</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J87  </td> <td>Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators [See also <a href="msc2020.html?t=35R35&btn=Current">35R35</a>, <a href="msc2020.html?t=49J40&btn=Current">49J40</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J88  </td> <td>Unilateral problems for elliptic systems and systems of variational inequalities with elliptic operators [See also <a href="msc2020.html?t=35R35&btn=Current">35R35</a>, <a href="msc2020.html?t=49J40&btn=Current">49J40</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J91  </td> <td>Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J92  </td> <td>Quasilinear elliptic equations with <span class="MathTeX">$p$</span><script type="math/tex">p</script>-Laplacian</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J93  </td> <td>Quasilinear elliptic equations with mean curvature operator</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J94  </td> <td>Elliptic equations with infinity-Laplacian</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J96  </td> <td>Monge-Amp猫re equations {For complex Monge-Amp猫re operators, see <a href="msc2020.html?t=32W20&btn=Current">32W20</a>; for parabolic Monge-Amp猫re equations, see <a href="msc2020.html?t=35K96&btn=Current">35K96</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35J99  </td> <td>None of the above, but in this section</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K05  </td> <td>Heat equation</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K08  </td> <td>Heat kernel</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K10  </td> <td>Second-order parabolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K15  </td> <td>Initial value problems for second-order parabolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K20  </td> <td>Initial-boundary value problems for second-order parabolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K25  </td> <td>Higher-order parabolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K30  </td> <td>Initial value problems for higher-order parabolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K35  </td> <td>Initial-boundary value problems for higher-order parabolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K40  </td> <td>Second-order parabolic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K41  </td> <td>Higher-order parabolic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K45  </td> <td>Initial value problems for second-order parabolic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K46  </td> <td>Initial value problems for higher-order parabolic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K51  </td> <td>Initial-boundary value problems for second-order parabolic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K52  </td> <td>Initial-boundary value problems for higher-order parabolic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K55  </td> <td>Nonlinear parabolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K57  </td> <td>Reaction-diffusion equations {For diffusion processes and reaction effects, see <a href="msc2020.html?t=47D07&btn=Current">47D07</a>, <a href="msc2020.html?t=58J65&btn=Current">58J65</a>, <a href="msc2020.html?t=60J60&btn=Current">60J60</a>, <a href="msc2020.html?t=60J70&btn=Current">60J70</a>, <a href="msc2020.html?t=74N25&btn=Current">74N25</a>, <a href="msc2020.html?t=76R50&btn=Current">76R50</a>, <a href="msc2020.html?t=76V05&btn=Current">76V05</a>, <a href="msc2020.html?t=80A23&btn=Current">80A23</a>, <a href="msc2020.html?t=82B24&btn=Current">82B24</a>, <a href="msc2020.html?t=82C24&btn=Current">82C24</a>, <a href="msc2020.html?t=92E20&btn=Current">92E20</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K58  </td> <td>Semilinear parabolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K59  </td> <td>Quasilinear parabolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K60  </td> <td>Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K61  </td> <td>Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K65  </td> <td>Degenerate parabolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K67  </td> <td>Singular parabolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K70  </td> <td>Ultraparabolic equations, pseudoparabolic equations, etc.</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K85  </td> <td>Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators [See also <a href="msc2020.html?t=35R35&btn=Current">35R35</a>, <a href="msc2020.html?t=49J40&btn=Current">49J40</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K86  </td> <td>Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators [See also <a href="msc2020.html?t=35R35&btn=Current">35R35</a>, <a href="msc2020.html?t=49J40&btn=Current">49J40</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K87  </td> <td>Unilateral problems for parabolic systems and systems of variational inequalities with parabolic operators [See also <a href="msc2020.html?t=35R35&btn=Current">35R35</a>, <a href="msc2020.html?t=49J40&btn=Current">49J40</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K90  </td> <td>Abstract parabolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K91  </td> <td>Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K92  </td> <td>Quasilinear parabolic equations with <span class="MathTeX">$p$</span><script type="math/tex">p</script>-Laplacian</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K93  </td> <td>Quasilinear parabolic equations with mean curvature operator</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K96  </td> <td>Parabolic Monge-Amp猫re equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35K99  </td> <td>None of the above, but in this section</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L02  </td> <td>First-order hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L03  </td> <td>Initial value problems for first-order hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L04  </td> <td>Initial-boundary value problems for first-order hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L05  </td> <td>Wave equation</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L10  </td> <td>Second-order hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L15  </td> <td>Initial value problems for second-order hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L20  </td> <td>Initial-boundary value problems for second-order hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L25  </td> <td>Higher-order hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L30  </td> <td>Initial value problems for higher-order hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L35  </td> <td>Initial-boundary value problems for higher-order hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L40  </td> <td>First-order hyperbolic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L45  </td> <td>Initial value problems for first-order hyperbolic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L50  </td> <td>Initial-boundary value problems for first-order hyperbolic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L51  </td> <td>Second-order hyperbolic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L52  </td> <td>Initial value problems for second-order hyperbolic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L53  </td> <td>Initial-boundary value problems for second-order hyperbolic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L55  </td> <td>Higher-order hyperbolic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L56  </td> <td>Initial value problems for higher-order hyperbolic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L57  </td> <td>Initial-boundary value problems for higher-order hyperbolic systems</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L60  </td> <td>First-order nonlinear hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L65  </td> <td>Hyperbolic conservation laws</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L67  </td> <td>Shocks and singularities for hyperbolic equations [See also <a href="msc2020.html?t=58Kxx&btn=Current">58Kxx</a>, <a href="msc2020.html?t=74J40&btn=Current">74J40</a>, <a href="msc2020.html?t=76L05&btn=Current">76L05</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L70  </td> <td>Second-order nonlinear hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L71  </td> <td>Second-order semilinear hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L72  </td> <td>Second-order quasilinear hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L75  </td> <td>Higher-order nonlinear hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L76  </td> <td>Higher-order semilinear hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L77  </td> <td>Higher-order quasilinear hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L80  </td> <td>Degenerate hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L81  </td> <td>Singular hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L82  </td> <td>Pseudohyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L85  </td> <td>Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators [See also <a href="msc2020.html?t=35R35&btn=Current">35R35</a>, <a href="msc2020.html?t=49J40&btn=Current">49J40</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L86  </td> <td>Unilateral problems for nonlinear hyperbolic equations and variational inequalities with nonlinear hyperbolic operators [See also <a href="msc2020.html?t=35R35&btn=Current">35R35</a>, <a href="msc2020.html?t=49J40&btn=Current">49J40</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L87  </td> <td>Unilateral problems for hyperbolic systems and systems of variational inequalities with hyperbolic operators [See also <a href="msc2020.html?t=35R35&btn=Current">35R35</a>, <a href="msc2020.html?t=49J40&btn=Current">49J40</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L90  </td> <td>Abstract hyperbolic equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35L99  </td> <td>None of the above, but in this section</td> </tr> <tr class="current"> <td></td> <td></td> <td>35M10  </td> <td>PDEs of mixed type</td> </tr> <tr class="current"> <td></td> <td></td> <td>35M11  </td> <td>Initial value problems for PDEs of mixed type</td> </tr> <tr class="current"> <td></td> <td></td> <td>35M12  </td> <td>Boundary value problems for PDEs of mixed type</td> </tr> <tr class="current"> <td></td> <td></td> <td>35M13  </td> <td>Initial-boundary value problems for PDEs of mixed type</td> </tr> <tr class="current"> <td></td> <td></td> <td>35M30  </td> <td>Mixed-type systems of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35M31  </td> <td>Initial value problems for mixed-type systems of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35M32  </td> <td>Boundary value problems for mixed-type systems of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35M33  </td> <td>Initial-boundary value problems for mixed-type systems of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35M85  </td> <td>Unilateral problems for linear PDEs of mixed type and variational inequalities with partial differential operators of mixed type [See also <a href="msc2020.html?t=35R35&btn=Current">35R35</a>, <a href="msc2020.html?t=49J40&btn=Current">49J40</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35M86  </td> <td>Unilateral problems for nonlinear PDEs of mixed type and variational inequalities with nonlinear partial differential operators of mixed type [See also <a href="msc2020.html?t=35R35&btn=Current">35R35</a>, <a href="msc2020.html?t=49J40&btn=Current">49J40</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35M87  </td> <td>Unilateral problems for mixed-type systems of PDEs and systems of variational inequalities with partial differential operators of mixed type [See also <a href="msc2020.html?t=35R35&btn=Current">35R35</a>, <a href="msc2020.html?t=49J40&btn=Current">49J40</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35M99  </td> <td>None of the above, but in this section</td> </tr> <tr class="current"> <td></td> <td></td> <td>35N05  </td> <td>Overdetermined systems of PDEs with constant coefficients</td> </tr> <tr class="current"> <td></td> <td></td> <td>35N10  </td> <td>Overdetermined systems of PDEs with variable coefficients</td> </tr> <tr class="current"> <td></td> <td></td> <td>35N15  </td> <td><span class="MathTeX">$\overline\partial$</span><script type="math/tex">\overline\partial</script>-Neumann problems and formal complexes in context of PDEs [See also <a href="msc2020.html?t=32W05&btn=Current">32W05</a>, <a href="msc2020.html?t=32W10&btn=Current">32W10</a>, <a href="msc2020.html?t=58J10&btn=Current">58J10</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35N20  </td> <td>Overdetermined initial value problems for PDEs and systems of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35N25  </td> <td>Overdetermined boundary value problems for PDEs and systems of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35N30  </td> <td>Overdetermined initial-boundary value problems for PDEs and systems of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35N99  </td> <td>None of the above, but in this section</td> </tr> <tr class="current"> <td></td> <td></td> <td>35P05  </td> <td>General topics in linear spectral theory for PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35P10  </td> <td>Completeness of eigenfunctions and eigenfunction expansions in context of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35P15  </td> <td>Estimates of eigenvalues in context of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35P20  </td> <td>Asymptotic distributions of eigenvalues in context of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35P25  </td> <td>Scattering theory for PDEs [See also <a href="msc2020.html?t=47A40&btn=Current">47A40</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35P30  </td> <td>Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35P99  </td> <td>None of the above, but in this section</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q05  </td> <td>Euler-Poisson-Darboux equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q07  </td> <td>Fuchsian PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q15  </td> <td>Riemann-Hilbert problems in context of PDEs [See also <a href="msc2020.html?t=30E25&btn=Current">30E25</a>, <a href="msc2020.html?t=31A25&btn=Current">31A25</a>, <a href="msc2020.html?t=31B20&btn=Current">31B20</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q20  </td> <td>Boltzmann equations {For fluid mechanics, see <a href="msc2020.html?t=76P05&btn=Current">76P05</a>; for statistical mechanics, see <a href="msc2020.html?t=82B40&btn=Current">82B40</a>, <a href="msc2020.html?t=82C40&btn=Current">82C40</a>, <a href="msc2020.html?t=82D05&btn=Current">82D05</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q30  </td> <td>Navier-Stokes equations {For fluid mechanics, see <a href="msc2020.html?t=76D05&btn=Current">76D05</a>, <a href="msc2020.html?t=76D07&btn=Current">76D07</a>, <a href="msc2020.html?t=76N10&btn=Current">76N10</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q31  </td> <td>Euler equations {For fluid mechanics, see <a href="msc2020.html?t=76D05&btn=Current">76D05</a>, <a href="msc2020.html?t=76D07&btn=Current">76D07</a>, <a href="msc2020.html?t=76N10&btn=Current">76N10</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q35  </td> <td>PDEs in connection with fluid mechanics</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q40  </td> <td>PDEs in connection with quantum mechanics</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q41  </td> <td>Time-dependent Schr枚dinger equations and Dirac equations {For quantum theory, see <a href="msc2020.html?t=81Q05&btn=Current">81Q05</a>; for relativity and gravitational theory, see <a href="msc2020.html?t=83A05&btn=Current">83A05</a>, <a href="msc2020.html?t=83C10&btn=Current">83C10</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q49  </td> <td>Transport equations {For calculus of variations and optimal control, see <a href="msc2020.html?t=49Q22&btn=Current">49Q22</a>; for fluid mechanics, see <a href="msc2020.html?t=76F25&btn=Current">76F25</a>; for statistical mechanics, see <a href="msc2020.html?t=82C70&btn=Current">82C70</a>, <a href="msc2020.html?t=82D75&btn=Current">82D75</a>; for operations research, see <a href="msc2020.html?t=90B06&btn=Current">90B06</a>; for mathematical programming, see <a href="msc2020.html?t=90C08&btn=Current">90C08</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q51  </td> <td>Soliton equations {For dynamical systems and ergodic theory, see <a href="msc2020.html?t=37K40&btn=Current">37K40</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q53  </td> <td>KdV equations (Korteweg-de Vries equations) {For dynamical systems and ergodic theory, see <a href="msc2020.html?t=37K10&btn=Current">37K10</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q55  </td> <td>NLS equations (nonlinear Schr枚dinger equations) {For dynamical systems and ergodic theory, see <a href="msc2020.html?t=37K10&btn=Current">37K10</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q56  </td> <td>Ginzburg-Landau equations {For optics and electromagnetic theory, see <a href="msc2020.html?t=78A25&btn=Current">78A25</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q60  </td> <td>PDEs in connection with optics and electromagnetic theory</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q61  </td> <td>Maxwell equations {For optics and electromagnetic theory, see <a href="msc2020.html?t=78A25&btn=Current">78A25</a>; for relativity and gravitational theory, see <a href="msc2020.html?t=83C22&btn=Current">83C22</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q62  </td> <td>PDEs in connection with statistics</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q68  </td> <td>PDEs in connection with computer science</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q70  </td> <td>PDEs in connection with mechanics of particles and systems of particles</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q74  </td> <td>PDEs in connection with mechanics of deformable solids</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q75  </td> <td>PDEs in connection with relativity and gravitational theory</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q76  </td> <td>Einstein equations {For several complex variables and analytic spaces, see <a href="msc2020.html?t=32Q40&btn=Current">32Q40</a>; for differential geometry, see <a href="msc2020.html?t=53C07&btn=Current">53C07</a>; for relativity and gravitational theory, see <a href="msc2020.html?t=83C05&btn=Current">83C05</a>, <a href="msc2020.html?t=83C25&btn=Current">83C25</a>, <a href="msc2020.html?t=83D05&btn=Current">83D05</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q79  </td> <td>PDEs in connection with classical thermodynamics and heat transfer</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q81  </td> <td>PDEs in connection with semiconductor devices {For statistical mechanics, see <a href="msc2020.html?t=82D37&btn=Current">82D37</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q82  </td> <td>PDEs in connection with statistical mechanics</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q83  </td> <td>Vlasov equations {For statistical mechanics, see <a href="msc2020.html?t=82C70&btn=Current">82C70</a>, <a href="msc2020.html?t=82D75&btn=Current">82D75</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q84  </td> <td>Fokker-Planck equations {For fluid mechanics, see <a href="msc2020.html?t=76X05&btn=Current">76X05</a>, <a href="msc2020.html?t=76W05&btn=Current">76W05</a>; for statistical mechanics, see <a href="msc2020.html?t=82C31&btn=Current">82C31</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q85  </td> <td>PDEs in connection with astronomy and astrophysics</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q86  </td> <td>PDEs in connection with geophysics</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q89  </td> <td>PDEs in connection with mean field game theory {For calculus of variations and optimal control, see <a href="msc2020.html?t=49N80&btn=Current">49N80</a>; for game theory, see <a href="msc2020.html?t=91A16&btn=Current">91A16</a>}</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q90  </td> <td>PDEs in connection with mathematical programming</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q91  </td> <td>PDEs in connection with game theory, economics, social and behavioral sciences</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q92  </td> <td>PDEs in connection with biology, chemistry and other natural sciences</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q93  </td> <td>PDEs in connection with control and optimization</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q94  </td> <td>PDEs in connection with information and communication</td> </tr> <tr class="current"> <td></td> <td></td> <td>35Q99  </td> <td>None of the above, but in this section</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R01  </td> <td>PDEs on manifolds [See also <a href="msc2020.html?t=32Wxx&btn=Current">32Wxx</a>, <a href="msc2020.html?t=53Cxx&btn=Current">53Cxx</a>, <a href="msc2020.html?t=58Jxx&btn=Current">58Jxx</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R02  </td> <td>PDEs on graphs and networks (ramified or polygonal spaces)</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R03  </td> <td>PDEs on Heisenberg groups, Lie groups, Carnot groups, etc.</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R05  </td> <td>PDEs with low regular coefficients and/or low regular data</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R06  </td> <td>PDEs with measure</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R07  </td> <td>PDEs on time scales</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R09  </td> <td>Integro-partial differential equations [See also <a href="msc2020.html?t=34K30&btn=Current">34K30</a>, <a href="msc2020.html?t=45K05&btn=Current">45K05</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R10  </td> <td>Partial functional-differential equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R11  </td> <td>Fractional partial differential equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R12  </td> <td>Impulsive partial differential equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R13  </td> <td>Fuzzy partial differential equations</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R15  </td> <td>PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) [See also <a href="msc2020.html?t=46Gxx&btn=Current">46Gxx</a>, <a href="msc2020.html?t=58D25&btn=Current">58D25</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R20  </td> <td>Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions) [See also <a href="msc2020.html?t=34Gxx&btn=Current">34Gxx</a>, <a href="msc2020.html?t=47A50&btn=Current">47A50</a>, <a href="msc2020.html?t=47D03&btn=Current">47D03</a>, <a href="msc2020.html?t=47D06&btn=Current">47D06</a>, <a href="msc2020.html?t=47D09&btn=Current">47D09</a>, <a href="msc2020.html?t=47H20&btn=Current">47H20</a>, <a href="msc2020.html?t=47Jxx&btn=Current">47Jxx</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R25  </td> <td>Ill-posed problems for PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R30  </td> <td>Inverse problems for PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R35  </td> <td>Free boundary problems for PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R37  </td> <td>Moving boundary problems for PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R45  </td> <td>Partial differential inequalities and systems of partial differential inequalities</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R50  </td> <td>PDEs of infinite order</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R60  </td> <td>PDEs with randomness, stochastic partial differential equations [See also <a href="msc2020.html?t=60H15&btn=Current">60H15</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R70  </td> <td>PDEs with multivalued right-hand sides</td> </tr> <tr class="current"> <td></td> <td></td> <td>35R99  </td> <td>None of the above, but in this section</td> </tr> <tr class="current"> <td></td> <td></td> <td>35S05  </td> <td>Pseudodifferential operators as generalizations of partial differential operators [See also <a href="msc2020.html?t=32W25&btn=Current">32W25</a>, <a href="msc2020.html?t=47G30&btn=Current">47G30</a>, <a href="msc2020.html?t=47L80&btn=Current">47L80</a>, <a href="msc2020.html?t=58J40&btn=Current">58J40</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35S10  </td> <td>Initial value problems for PDEs with pseudodifferential operators</td> </tr> <tr class="current"> <td></td> <td></td> <td>35S15  </td> <td>Boundary value problems for PDEs with pseudodifferential operators</td> </tr> <tr class="current"> <td></td> <td></td> <td>35S16  </td> <td>Initial-boundary value problems for PDEs with pseudodifferential operators</td> </tr> <tr class="current"> <td></td> <td></td> <td>35S30  </td> <td>Fourier integral operators applied to PDEs [See also <a href="msc2020.html?t=43A32&btn=Current">43A32</a>, <a href="msc2020.html?t=58J40&btn=Current">58J40</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35S35  </td> <td>Topological aspects for pseudodifferential operators in context of PDEs: intersection cohomology, stratified sets, etc. [See also <a href="msc2020.html?t=32C38&btn=Current">32C38</a>, <a href="msc2020.html?t=32S40&btn=Current">32S40</a>, <a href="msc2020.html?t=32S60&btn=Current">32S60</a>, <a href="msc2020.html?t=58J15&btn=Current">58J15</a>]</td> </tr> <tr class="current"> <td></td> <td></td> <td>35S50  </td> <td>Paradifferential operators as generalizations of partial differential operators in context of PDEs</td> </tr> <tr class="current"> <td></td> <td></td> <td>35S99  </td> <td>None of the above, but in this section</td> </tr> </table> <div class="buttonBox"> <input type="submit" name="btn" value="Clear" class="button" /> </div> <span class="legend"> < <a href="msc2020.html?t=34-XX&btn=Current">34-XX</a> | <a href="msc2020.html?t=&btn=Current">Up</a> | <a href="msc2020.html?t=37-XX&btn=Current">37-XX</a> > </span> </div> </form> </div> <div class="folderFooter"><div class="left"> </div><div class="right"> </div></div> </div> </div> </div> <div class="copyright"> <a href="http://www.ams.org/ams/copyright.html">© Copyright 2024, American Mathematical Society</a><br 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