Document Zbl 1326.74101

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The novelty consists in the structure of the inequalities which involve two history-dependent operators and two nondifferentiable functionals, a convex and a nonconvex one. For these inequalities we provide an existence and uniqueness result of the solution. The proof is based on arguments of surjectivity for pseudomonotone operators and fixed point. Then, we consider a viscoelastic problem in which the contact is frictionless and is modeled with a new boundary condition which describes both the instantaneous and the memory effects of the foundation. We prove that this problem leads to a history-dependent variational-hemivariational inequality in which the unknown is the displacement field. We apply our abstract result in order to prove the unique weak solvability of this viscoelastic contact problem.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A6373735">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A6373735">Cited in <strong>58</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A74M15" title="MSC2020">74M15</a> </td> <td class="space"> Contact in solid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A49J40" title="MSC2020">49J40</a> </td> <td class="space"> Variational inequalities </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74H20" title="MSC2020">74H20</a> </td> <td class="space"> Existence of solutions of dynamical problems in solid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74H25" title="MSC2020">74H25</a> </td> <td class="space"> Uniqueness of solutions of dynamical problems in solid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74M10" title="MSC2020">74M10</a> </td> <td class="space"> Friction in solid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74D05" title="MSC2020">74D05</a> </td> <td class="space"> Linear constitutive equations for materials with memory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Avariational-hemivariational+inequality">variational-hemivariational inequality</a>; <a href="/?q=ut%3AClarke+subdifferential">Clarke subdifferential</a>; <a href="/?q=ut%3Ahistory-dependent+operator">history-dependent operator</a>; <a href="/?q=ut%3Aviscoelastic+material">viscoelastic material</a>; <a href="/?q=ut%3Africtionless+contact">frictionless contact</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 1326.74101" data-ciurl="/ci/06373735" data-biburl="/bibtex/06373735.bib" data-amsurl="/amsrefs/06373735.bib" data-xmlurl="/xml/06373735.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06373735.pdf" title="Zbl 1326.74101 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.nonrwa.2014.09.021" aria-label="DOI for “History-dependent variational-hemivariational inequalities in contact mechanics”" title="10.1016/j.nonrwa.2014.09.021">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">Baiocchi, C.; Capelo, A., Variational and Quasivariational Inequalities: Applications to Free-Boundary Problems (1984), John Wiley: John Wiley Chichester · <a href="/0551.49007" class="nowrap">Zbl 0551.49007</a></td> </tr><tr> <td>[2]</td> <td class="space">Barbu, V., Optimal Control of Variational Inequalities (1984), Pitman: Pitman Boston · <a href="/0574.49005" class="nowrap">Zbl 0574.49005</a></td> </tr><tr> <td>[3]</td> <td class="space">Brézis, H., Equations et inéquations non linéaires dans les espaces vectoriels en dualité, Ann. 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