Document Zbl 1515.93033

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Control Signals Syst.</a> <a href="/?q=in%3A492536" title="Articles in this Issue">35, No. 1, 77-123 (2023)</a>. </div> <div class="abstract">The paper presented a simpler proof of the exact boundary controllability which is not based on the cost of observability of the wave equation with respect to potentials, and show that the above fixed point application is contracting yielding a constructive method to approximate the controls for the semilinear equation. The paper is interesting and well-orginized. The proposed results improved the exisitng results. Many experiments are carried out to show the corrtness of the proposed results. The results can be extended to the multi-dimensional case and for nonlinearities involving the gradient of the solution<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A18830">Liping Chen (Hefei)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7653182">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B05" title="MSC2020">93B05</a> </td> <td class="space"> Controllability </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C20" title="MSC2020">93C20</a> </td> <td class="space"> Control/observation systems governed by partial differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35L71" title="MSC2020">35L71</a> </td> <td class="space"> Second-order semilinear hyperbolic equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Asemilinear+wave+equation">semilinear wave equation</a>; <a href="/?q=ut%3Aexact+boundary+controllability">exact boundary controllability</a>; <a href="/?q=ut%3ACarleman+estimates">Carleman estimates</a>; <a href="/?q=ut%3Afixed+point">fixed point</a></div> <div class="software"> <h3>Software:</h3><a href="/software/1436">FreeFem++</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 1515.93033" data-ciurl="/ci/07653182" data-biburl="/bibtex/07653182.bib" data-amsurl="/amsrefs/07653182.bib" data-xmlurl="/xml/07653182.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07653182.pdf" title="Zbl 1515.93033 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/s00498-022-00331-4" aria-label="DOI for “Exact boundary controllability of 1D semilinear wave equations through a constructive approach”" title="10.1007/s00498-022-00331-4">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://hal.science/hal-03599036" title="Open Access at HAL">HAL </a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Baudouin, L.; De Buhan, M.; Ervedoza, S., Global Carleman estimates for waves and applications, Commun Partial Differ Equ, 38, 5, 823-859 (2013) · <a href="/1267.93027" class="nowrap">Zbl 1267.93027</a> · <a href="https://doi.org/10.1080/03605302.2013.771659" class="nowrap">doi:10.1080/03605302.2013.771659</a></td> </tr><tr> <td>[2]</td> <td class="space">Burman E, Feizmohammadi A, Münch A, Oksanen L (2021) Space time finite element methods for control problems subject to the wave equation. 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