Comparison results for a class of quasilinear evolutionary hemivariational inequalities

Siegfried Carl

doi:10.3934/proc.2007.2007.221

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2007, Volume 2007: 221-229. Doi: 10.3934/proc.2007.2007.221 open access

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Comparison results for a class of quasilinear evolutionary hemivariational inequalities

Siegfried Carl^1,

1.
Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle

Received: August 31, 2006

Revised: February 28, 2007

Published: August 2007

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Abstract

We consider a class of quasilinear evolutionary hemivariational inequalities under nonmonotone multivalued flux boundary conditions. Our main goal is to provide existence and comparison results in terms of appropriately defined sub- and supersolutions on the basis of which one can prove compactness and extremality results of the solution set within the sector of sub- and supersolutions.

Keywords:

Evolutionary hemivariational inequality,
sub-supersolution,
comparison,
extremal solution,
compactness.

Mathematics Subject Classification: Primary: 35K55, 47H04, 47J35; Secondary: 35R70.

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