Document Zbl 1073.35040

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Model. Numer. Anal.</a> <a href="/?q=in%3A99531" title="Articles in this Issue">36, No. 4, 657-691 (2002)</a>. </div> <div class="abstract">Authors’ abstract: We consider a dynamical one-dimensional nonlinear von Kármán model for beams depending on a parameter $\varepsilon > 0$ and study its asymptotic behavior for $t$ large, as $\varepsilon \to 0$. Introducing appropriate damping mechanisms we show that the energy of solutions of the corresponding damped models decay exponentially uniformly with respect to the parameter $\varepsilon $. In order for this to be true the damping mechanism has to have the appropriate scale with respect to $\varepsilon $. In the limit as $\varepsilon \to 0$ we obtain damped Berger-Timoshenko beam models for which the energy tends to zero exponentially as well. This is done both in the case of internal and boundary damping. We address the same problem for plates with internal damping.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A2677">Sergiu Aizicovici (Athens/Ohio)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A1970464">Cited in <strong>11</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A35B40" title="MSC2020">35B40</a> </td> <td class="space"> Asymptotic behavior of solutions to PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35Q74" title="MSC2020">35Q74</a> </td> <td class="space"> PDEs in connection with mechanics of deformable solids </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74B20" title="MSC2020">74B20</a> </td> <td class="space"> Nonlinear elasticity </td> </tr><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%3A74K20" title="MSC2020">74K20</a> </td> <td class="space"> Plates </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Auniform+stabilization">uniform stabilization</a>; <a href="/?q=ut%3Asingular+limit">singular limit</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 1073.35040" data-ciurl="/ci/01970464" data-biburl="/bibtex/01970464.bib" data-amsurl="/amsrefs/01970464.bib" data-xmlurl="/xml/01970464.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/01970464.pdf" title="Zbl 1073.35040 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/10.1051/m2an:2002029" aria-label="DOI for “Stabilization of Berger-Timoshenko's equation as limit of the uniform stabilization of the von Kármán system of beams and plates.”" title="10.1051/m2an:2002029">DOI</a> <a class="btn btn-default btn-xs" type="button" href="http://www.numdam.org/item?id=M2AN_2002__36_4_657_0" title="Open Access at Numdam">Numdam</a> <a class="btn btn-default btn-xs" type="button" href="https://eudml.org/doc/194120" title="Open Access at EuDML">EuDML</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">J.M. 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