Document Zbl 0942.35110

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Differ. Equations</a> <a href="/?q=in%3A57285" title="Articles in this Issue">155, No. 1, 89-132 (1999)</a>. </div> <div class="abstract">This paper deals with initial value problems for nonlinear first-order hyperbolic systems \[ \partial_t U + \sum_{j=1}^{n} A_{j}(U)\partial_{x_j} U = Q(U)/\varepsilon \] where $U=U(x,t):\mathbb{R}^n\times[0,\infty) \to \mathbb{R}^n$ is the unknown vector function. Here $0<\varepsilon \ll 1$ is a small parameter, and the nonlinear term $Q(U)/\varepsilon$ represents a stiff source term. Under a suitable structural stability condition the author constructs formal asymptotic expansions of solutions having an initial layer. This structural condition is equivalent to the well-known subcharacteristic condition for $2\times 2$ one-dimensional hyperbolic systems. Convergence of asymptotic expansions is proven. The theory developed in this paper can be applied to several problems arising from mathematical physics like e.g. equations of kinetic gas theory, reacting flow models, relativistic magnetohydrodynamic equations etc.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A7746">Daniel Ševčovič (Bratislava)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A1309593">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A1309593">Cited in <strong>109</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A35L60" title="MSC2020">35L60</a> </td> <td class="space"> First-order nonlinear hyperbolic equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35B25" title="MSC2020">35B25</a> </td> <td class="space"> Singular perturbations in context of PDEs </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aformal+asymptotic+expansions">formal asymptotic expansions</a>; <a href="/?q=ut%3Azero+relaxation+limit">zero relaxation limit</a>; <a href="/?q=ut%3Ainitial+layer">initial layer</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 0942.35110" data-ciurl="/ci/01309593" data-biburl="/bibtex/01309593.bib" data-amsurl="/amsrefs/01309593.bib" data-xmlurl="/xml/01309593.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/01309593.pdf" title="Zbl 0942.35110 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1006/jdeq.1998.3584" aria-label="DOI for “Singular perturbations of first-order hyperbolic systems with stiff source terms”" title="10.1006/jdeq.1998.3584">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://semanticscholar.org/paper/879a5a2c2dabb9e3c3b961bda7651a9983ae385a" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Caflisch, R.; Papanicolaou, G. C., The fluid-dynamical limit of a nonlinear model Boltzmann equation, Comm. Pure Appl. Math., 32, 589-616 (1979) · <a href="/0438.76059" class="nowrap">Zbl 0438.76059</a></td> </tr><tr> <td>[2]</td> <td class="space">Chen, G.-Q.; Levermore, C. D.; Liu, T.-P., Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math., 47, 787-830 (1994) · <a href="/0806.35112" class="nowrap">Zbl 0806.35112</a></td> </tr><tr> <td>[3]</td> <td class="space">Chen, G.-Q.; Liu, T.-P., Zero relaxation and dissipation limits for hyperbolic conservation laws, Comm. Pure Appl. Math., 46, 755-781 (1993) · <a href="/0797.35113" class="nowrap">Zbl 0797.35113</a></td> </tr><tr> <td>[4]</td> <td class="space">Eckhaus, W., Matching principles and composite expansions, Lecture Notes in Math. (1977), Springer-Verlag: Springer-Verlag Berlin, p. 146-177 · <a href="/0374.35007" class="nowrap">Zbl 0374.35007</a></td> </tr><tr> <td>[5]</td> <td class="space">Geel, R., Singular Perturbations of Hyperbolic Type (1978), University of AmsterdamMathematisch Centrum · <a href="/0498.35001" class="nowrap">Zbl 0498.35001</a></td> </tr><tr> <td>[6]</td> <td class="space">Gu, Z.-M.; Nefedov, N. N.; O’Malley, R. E., On singular singularly perturbed initial value problems, SIAM J. Appl. Math., 49, 1-25 (1989) · <a href="/0676.34038" class="nowrap">Zbl 0676.34038</a></td> </tr><tr> <td>[7]</td> <td class="space">Van Harten, A.; Van Hassel, R. R., A quasilinear, singular perturbation problem of hyperbolic type, SIAM J. Math. Anal., 16, 1258-1267 (1985) · <a href="/0612.35007" class="nowrap">Zbl 0612.35007</a></td> </tr><tr> <td>[8]</td> <td class="space">de Jager, E. M., Singular perturbations of hyperbolic type, Nieuw Arch. Wisk., 23, 145-172 (1975) · <a href="/0304.35007" class="nowrap">Zbl 0304.35007</a></td> </tr><tr> <td>[9]</td> <td class="space">Jin, S.; Xin, Z., The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Comm. Pure Appl. Math., 48, 235-277 (1995) · <a href="/0826.65078" class="nowrap">Zbl 0826.65078</a></td> </tr><tr> <td>[10]</td> <td class="space">John, F., Partial Differential Equations (1982), Springer-Verlag: Springer-Verlag New York · <a href="/0472.35001" class="nowrap">Zbl 0472.35001</a></td> </tr><tr> <td>[11]</td> <td class="space">Kato, T., The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Rational Mech. Anal., 58, 181-205 (1975) · <a href="/0343.35056" class="nowrap">Zbl 0343.35056</a></td> </tr><tr> <td>[12]</td> <td class="space">Kreiss, H.-O., Problems with different time scales for partial differential equations, Comm. Pure Appl. Math., 33, 399-439 (1980) · <a href="/0439.35043" class="nowrap">Zbl 0439.35043</a></td> </tr><tr> <td>[13]</td> <td class="space">LeVeque, R. J.; Roe, P.; van Leer, B.; Yee, H. C., Final Report (1989)</td> </tr><tr> <td>[14]</td> <td class="space">Liu, T.-P., Hyperbolic conservation laws with relaxation, Comm. Math. Phys., 108, 153-175 (1987) · <a href="/0633.35049" class="nowrap">Zbl 0633.35049</a></td> </tr><tr> <td>[15]</td> <td class="space">Majda, A., Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables (1984), Springer-Verlag: Springer-Verlag New York · <a href="/0537.76001" class="nowrap">Zbl 0537.76001</a></td> </tr><tr> <td>[16]</td> <td class="space">R. Natalini, Recent mathematical results on hyperbolic relaxation problems, in, Analysis of systems of conservation laws, (, H. Freistühler, Ed.), Pitman Research Notes in Mathematics Series, Longman, Harlow, in press.; R. Natalini, Recent mathematical results on hyperbolic relaxation problems, in, Analysis of systems of conservation laws, (, H. Freistühler, Ed.), Pitman Research Notes in Mathematics Series, Longman, Harlow, in press.</td> </tr><tr> <td>[17]</td> <td class="space">O’Malley, R. E., Introduction to Singular Perturbations (1974), Academic Press: Academic Press New York · <a href="/0287.34062" class="nowrap">Zbl 0287.34062</a></td> </tr><tr> <td>[18]</td> <td class="space">Platkowski, T.; Illner, R., Discrete velocity models of the Boltzmann equation: A survey on the mathematical aspects of the theory, SIAM Rev., 30, 213-255 (1988) · <a href="/0668.76087" class="nowrap">Zbl 0668.76087</a></td> </tr><tr> <td>[19]</td> <td class="space">Rosemann, J. J.; Meyer, R. E., Hyperbolic-hyperbolc systems, J. Differential Equations, 10, 403-411 (1970) · <a href="/0206.40001" class="nowrap">Zbl 0206.40001</a></td> </tr><tr> <td>[20]</td> <td class="space">Schochet, S., Hyperbolic-hyperbolic singular limits, Comm. Partial Differential Equations, 12, 589-632 (1987) · <a href="/0629.35079" class="nowrap">Zbl 0629.35079</a></td> </tr><tr> <td>[21]</td> <td class="space">Whitham, J., Linear and Nonlinear Waves (1974), Wiley: Wiley New York · <a href="/0373.76001" class="nowrap">Zbl 0373.76001</a></td> </tr><tr> <td>[22]</td> <td class="space">Yong, W.-A., Singular Perturbations of First-Order Hyperbolic Systems (1992), Universität Heidelberg</td> </tr><tr> <td>[23]</td> <td class="space">Yong, W.-A., Existence and asymptotic stability of traveling wave solutions of a model system for reacting flow, Nonlinear Anal., 26, 1791-1809 (1996) · <a href="/0873.76092" class="nowrap">Zbl 0873.76092</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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