Document Zbl 1046.74028

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Math. Comput.</a> <a href="/?q=in%3A101659" title="Articles in this Issue">148, No. 2, 475-496 (2004)</a>. </div> <div class="abstract">Summary: We study the stability of solutions for Kirchhoff plate equations with a memory condition working at the boundary. We show that such dissipation is strong enough to produce exponential decay of the solution, provided the relaxation functions also decays exponentially. When the relaxation functions decays polynomially, we show that the solution decays polynomially and with the same rate.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A2019682">Cited in <strong>42</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A74K10" title="MSC2020">74K10</a> </td> <td class="space"> Rods (beams, columns, shafts, arches, rings, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74H40" title="MSC2020">74H40</a> </td> <td class="space"> Long-time behavior of solutions for dynamical problems in solid mechanics </td> </tr><tr> <td class="mono"> 35Q72 </td> <td class="space"> Other PDE from mechanics (MSC2000) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Apolynomial+decay">polynomial decay</a>; <a href="/?q=ut%3Astrong+solution">strong solution</a>; <a href="/?q=ut%3AGalerkin+approximation">Galerkin approximation</a>; <a href="/?q=ut%3Aexponential+decay">exponential decay</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 1046.74028" data-ciurl="/ci/02019682" data-biburl="/bibtex/02019682.bib" data-amsurl="/amsrefs/02019682.bib" data-xmlurl="/xml/02019682.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/02019682.pdf" title="Zbl 1046.74028 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/10.1016/S0096-3003(02)00915-3" aria-label="DOI for “A boundary condition with memory for Kirchhoff plate equations.”" title="10.1016/S0096-3003(02)00915-3">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Ji, G.; Lasiecka, I., Nonlinear boundary feedback stabilization for a semilinear Kirchhoff plate with dissipation acting only via moments-limiting behavior, Journal of Mathematical Analysis and Applications, 229, 452-479 (1999) · <a href="/0922.35099" class="nowrap">Zbl 0922.35099</a></td> </tr><tr> <td>[2]</td> <td class="space">Lasiecka, I., Exponential decay rates for the solutions of Euler-Bernoulli moments only, Journal of Differential Equations, 95, 169-182 (1992) · <a href="/0757.35057" class="nowrap">Zbl 0757.35057</a></td> </tr><tr> <td>[3]</td> <td class="space">Lasiecka, I.; Triggiani, R., Sharp trace estimates of solutions to Kirchhoff and Euler-Bernoulli equations, Applied Mathematics and Optimization, 28, 277-306 (1993) · <a href="/0789.35155" class="nowrap">Zbl 0789.35155</a></td> </tr><tr> <td>[4]</td> <td class="space">Lagnese, J. E., Asymptotic energy estimates for Kirchhoff plates subject to weak viscoelastic damping, (International Series of Numerical Mathematics, vol. 91 (1989), Birkhäuser-Verlag: Birkhäuser-Verlag Bassel) · <a href="/0718.35011" class="nowrap">Zbl 0718.35011</a></td> </tr><tr> <td>[5]</td> <td class="space">Lagnese, J. E., Boundary Stabilization of Thin Plates (1989), SIAM. Society for industrial and Applied Mathematics: SIAM. Society for industrial and Applied Mathematics Philadelphia, PA · <a href="/0682.73009" class="nowrap">Zbl 0682.73009</a></td> </tr><tr> <td>[6]</td> <td class="space">Lagnese, J. E.; Lions, J. L., Modelling analysis of thin plates, (Celletion Recherches en Mathématiques Appliquées 6 (1989), Masson: Masson Paris) · <a href="/0662.73039" class="nowrap">Zbl 0662.73039</a></td> </tr><tr> <td>[7]</td> <td class="space">Lions, J. L.; Magenes, E., (Non-Homoneous Boundary Value Problem and Applications, vol. I (1972), Springer-Verlag: Springer-Verlag New York) · <a href="/0227.35001" class="nowrap">Zbl 0227.35001</a></td> </tr><tr> <td>[8]</td> <td class="space">Lions, J. L., Quelques Mèthodes de resolution de problèmes aux limites non lineaires (1969), Dunod Gauthiers Villars: Dunod Gauthiers Villars Paris · <a href="/0189.40603" class="nowrap">Zbl 0189.40603</a></td> </tr><tr> <td>[9]</td> <td class="space">Horn, M. A., Uniform decay rates for the solution to the Euler Bernoulli plate equation with boundary feedback via benoling moments, Differential, Integral Equation, 6, 5, 1121-1150 (1992) · <a href="/0754.35177" class="nowrap">Zbl 0754.35177</a></td> </tr><tr> <td>[10]</td> <td class="space">Muñoz Rivera, J. E.; Lapa, E. C.; Barreto, R., Decay rates for viscoelastic plates with memory, Journal of Elasticity, 44, 61-87 (1996) · <a href="/0876.73037" class="nowrap">Zbl 0876.73037</a></td> </tr><tr> <td>[11]</td> <td class="space">Komornik, V., On the nonlinear boundary stabilization of Kirchhoff plates, Nonlinear Differential Equation and Applications, 1, 323-337 (1994) · <a href="/0818.35126" class="nowrap">Zbl 0818.35126</a></td> </tr><tr> <td>[12]</td> <td class="space">Racke, R., Lectures on nonlinear evolution equations. Initial value problems, (Aspect of Mathematics E19. Friedr. (1992), Vieweg & Sohn: Vieweg & Sohn Braunschweig/Wiesbaden) · <a href="/1329.35006" class="nowrap">Zbl 1329.35006</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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