Document Zbl 1391.35055

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Dyn. Control Syst.</a> <a href="/?q=in%3A383363" title="Articles in this Issue">24, No. 2, 313-323 (2018)</a>. </div> <div class="abstract">Summary: A nonlinear problem modeling a moving string with memory condition at the boundary is considered. This work aims at establishing reasonable sufficient conditions capable of suppressing the transversal vibrations that occur during the movement of the string. Unlike the fixed strings case here we need to employ the Reynold Transport Theorem to compute the “total” derivative. This results in the appearance of several boundary terms which necessitates appropriate handling. We shall prove that the motion of the string plays an important role in determining the rate of the decay of solutions.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6859813">Cited in <strong>12</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%3A35L20" title="MSC2020">35L20</a> </td> <td class="space"> Initial-boundary value problems for second-order hyperbolic equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A45K05" title="MSC2020">45K05</a> </td> <td class="space"> Integro-partial differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74K05" title="MSC2020">74K05</a> </td> <td class="space"> Strings </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35Q93" title="MSC2020">35Q93</a> </td> <td class="space"> PDEs in connection with control and optimization </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Atransversal+displacement">transversal displacement</a>; <a href="/?q=ut%3Auniform+decay">uniform 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 1391.35055" data-ciurl="/ci/06859813" data-biburl="/bibtex/06859813.bib" data-amsurl="/amsrefs/06859813.bib" data-xmlurl="/xml/06859813.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06859813.pdf" title="Zbl 1391.35055 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/10.1007/s10883-017-9370-y" aria-label="DOI for “Uniform stabilization of a nonlinear axially moving string by a boundary control of memory type”" title="10.1007/s10883-017-9370-y">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">Aassila M, Cavalcanti M M, Soriano J A. 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