Document Zbl 1514.35390

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A.</a>; <a href="/authors/araruna.fagner-dias" title="Author Profile">Araruna, Fágner D.</a>; <a href="/authors/santos.mauricio-cardoso" title="Author Profile">Santos, Maurício C.</a></div> <h2 class="title"> <strong>On a multi-objective control problem for the Korteweg-de Vries equation.</strong> <i>(English)</i> <a class="label nowrap" href="/1514.35390">Zbl 1514.35390</a> </h2> <div class="source"> <a href="/serials/1897" title="Journal Profile">Calc. Var. Partial Differ. Equ.</a> <a href="/?q=in%3A495361" title="Articles in this Issue">62, No. 4, Paper No. 131, 34 p. (2023)</a>. </div> <div class="abstract">Summary: This paper deals with a hierarchical control problem for the <span class="zbmathjax-textit">Korteweg-de Vries</span> (KdV) equation with distributed controls following a Stackelberg-Nash strategy. We have a control problem with many objectives to be achieved and, to do that, more than one control is needed. We assume that there is a primary control, called <span class="zbmathjax-textit">the leader</span>, and two secondary ones, called <span class="zbmathjax-textit">the followers</span>, each of them responsible for a given objective. Once the leader has fixed its goals, the followers must act to accomplish their ones. In the present paper, the leader wants to drive the solutions of a KdV equation to a given trajectory, while the followers must be in equilibrium according to their targets. We stress that results of this kind are already known for many parabolic and hyperbolic equations, but no results are known for any dispersive equation.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7672480">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%3A35Q53" title="MSC2020">35Q53</a> </td> <td class="space"> KdV equations (Korteweg-de Vries equations) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35Q35" title="MSC2020">35Q35</a> </td> <td class="space"> PDEs in connection with fluid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76B15" title="MSC2020">76B15</a> </td> <td class="space"> Water waves, gravity waves; dispersion and scattering, nonlinear interaction </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B05" title="MSC2020">93B05</a> </td> <td class="space"> Controllability </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ANash+equilibrium">Nash equilibrium</a>; <a href="/?q=ut%3AStackelberg%27s+method">Stackelberg’s method</a>; <a href="/?q=ut%3Anull+controllability">null controllability</a>; <a href="/?q=ut%3ACarleman+estimates">Carleman estimates</a>; <a href="/?q=ut%3AKdV+equation">KdV equation</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 1514.35390" data-ciurl="/ci/07672480" data-biburl="/bibtex/07672480.bib" data-amsurl="/amsrefs/07672480.bib" data-xmlurl="/xml/07672480.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07672480.pdf" title="Zbl 1514.35390 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/s00526-023-02471-0" aria-label="DOI for “On a multi-objective control problem for the Korteweg-de Vries equation”" title="10.1007/s00526-023-02471-0">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">Alekseev, V.M., Tikhomirov, V.M., Fomin, S.V.: Optimal Control. 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