Document Zbl 1372.35008

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Differ. Equations</a> <a href="/?q=in%3A368699" title="Articles in this Issue">263, No. 7, 3989-4006 (2017)</a>. </div> <div class="abstract">Summary: In this paper, we firstly introduce a complicated system obtained by mixing a nonlinear evolutionary partial differential equation and a mixed variational inequality in infinite dimensional Banach spaces in the case where the set of constraints is not necessarily bounded and the problem is driven by nonlocal boundary conditions, which is called partial differential variational inequality ((PDVI), for short). Then, we show that the solution set of the mixed variational inequality involved in problem (PDVI) is nonempty, bounded, closed and convex. Moreover, the upper semicontinuity and measurability properties for set-valued mapping $U : [0, T] \times E_2 \rightarrow C b v(E_1)$ (see (3.7), below) are also established. Finally, several existence results for (PDVI) are obtained by using a fixed point theorem for condensing set-valued operators and theory of measure of noncompactness.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6756306">Cited in <strong>118</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A35A01" title="MSC2020">35A01</a> </td> <td class="space"> Existence problems for PDEs: global existence, local existence, non-existence </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35R15" title="MSC2020">35R15</a> </td> <td class="space"> PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35K86" title="MSC2020">35K86</a> </td> <td class="space"> Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47D06" title="MSC2020">47D06</a> </td> <td class="space"> One-parameter semigroups and linear evolution equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3A%5C%28C_0%5C%29-semigroup">$C_0$-semigroup</a>; <a href="/?q=ut%3Ameasure+of+noncompactness">measure of noncompactness</a>; <a href="/?q=ut%3Anonlinear+evolutionary+partial+differential+equation">nonlinear evolutionary partial differential equation</a>; <a href="/?q=ut%3Amixed+variational+inequality">mixed variational inequality</a>; <a href="/?q=ut%3Anonlocal+boundary+conditions">nonlocal boundary conditions</a>; <a href="/?q=ut%3Aupper+semicontinuity">upper semicontinuity</a>; <a href="/?q=ut%3Afixed+point+theorem">fixed point theorem</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 1372.35008" data-ciurl="/ci/06756306" data-biburl="/bibtex/06756306.bib" data-amsurl="/amsrefs/06756306.bib" data-xmlurl="/xml/06756306.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06756306.pdf" title="Zbl 1372.35008 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/10.1016/j.jde.2017.05.010" aria-label="DOI for “Partial differential variational inequalities involving nonlocal boundary conditions in Banach spaces”" title="10.1016/j.jde.2017.05.010">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">Bothe, D., Multivalued perturbations of $m$-accretive differential inclusions, Israel J. 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