Document Zbl 1514.35032

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Korean Math. Soc.</a> <a href="/?q=in%3A496708" title="Articles in this Issue">60, No. 1, 257-279 (2023)</a>. </div> <div class="abstract">Summary: Applying the Lyapunov-Schmidt reduction, we consider spectral stability of small amplitude stationary periodic solutions bifurcating from an equilibrium of the generalized Swift-Hohenberg equation. We follow the mathematical framework developed in [<span class="zbmathjax-textit">A. Mielke</span>, in: Nonlinear dynamics and pattern formation in the natural environment. Proceedings of the international conference held in Noordwijkerhout, The Netherlands, July 4-7, 1994. Harlow: Longman; New York, NY: Wiley. 206–222 (1995; <a href="/0838.35011">Zbl 0838.35011</a>); Commun. Math. Phys. 189, No. 3, 829–853 (1997; <a href="/0897.76037">Zbl 0897.76037</a>); <span class="zbmathjax-textit">G. Schneider</span>, ibid. 178, No. 3, 679–702 (1996; <a href="/0861.35107">Zbl 0861.35107</a>); ibid. 178, No. 3, 679–702 (1996; <a href="/0861.35107">Zbl 0861.35107</a>)] to construct such periodic solutions and to determine regions in the parameter space for which they are stable by investigating the movement of the spectrum near zero as parameters vary.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A7688139">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A7688139">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%3A35B35" title="MSC2020">35B35</a> </td> <td class="space"> Stability in context of PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35B32" title="MSC2020">35B32</a> </td> <td class="space"> Bifurcations in context of PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35K58" title="MSC2020">35K58</a> </td> <td class="space"> Semilinear parabolic equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ageneralized+Swift-Hohenberg+equations">generalized Swift-Hohenberg equations</a>; <a href="/?q=ut%3ALyapunov-Schmidt+reduction">Lyapunov-Schmidt reduction</a>; <a href="/?q=ut%3Aspectral+stability">spectral stability</a>; <a href="/?q=ut%3Abifurcation+of+small+stationary+periodic+solutions">bifurcation of small stationary periodic solutions</a></div><div class="keywords"> <h3>Citations:</h3><a href="/0838.35011">Zbl 0838.35011</a>; <a href="/0897.76037">Zbl 0897.76037</a>; <a href="/0861.35107">Zbl 0861.35107</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 1514.35032" data-ciurl="/ci/07688139" data-biburl="/bibtex/07688139.bib" data-amsurl="/amsrefs/07688139.bib" data-xmlurl="/xml/07688139.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07688139.pdf" title="Zbl 1514.35032 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/10.4134/BKMS.b220116" aria-label="DOI for “Stability of bifurcating stationary periodic solutions of the generalized Swift-Hohenberg equation”" title="10.4134/BKMS.b220116">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">D. 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