Extremality in solving general quasilinear parabolic inclusions
type: Item
instance of: scholarly article
title: Extremality in solving general quasilinear parabolic inclusions
zbMATH Open document ID: 1069.35028
author: S. Carl
author: Dumitru Motreanu
published in: Journal of Optimization Theory and Applications
publication date: 2005-04-08T00:00:00Z
review text: This paper deals with initial boundary value problems for parabolic inclusions extending previous results by the same authors. More precisely, the multivalued term is a difference between the Clark generalized gradient of some locally Lipschitz function, verifying a unilateral growth condition, and the subdifferential of a convex function; the elliptic part is a quasilinear operator of Leray-Lions type. This type of differential inclusions has applications in solving problems with non-convex and non-smooth functionals in mechanics and in engineering. The authors, assuming the existence of an upper solution \(\overline u\) and a lower solution \(\underline u\) such that \(\underline u\leq\overline u\) and some conditions on the data, prove the existence of an extremal solution in the interval \([\underline u,\overline u]\), and the compactness of the solution set in a sector in adequate function spaces.
reviewed by: Maria Agostina Vivaldi
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K85
Mathematics Subject Classification ID: 35R70
zbMATH DE Number: 2154316
zbMATH Keywords: Leray-Lions-quasilinear operator
zbMATH Keywords: Clark generalized gradient of locally Lipschitz functions
zbMATH Keywords: upper solution
zbMATH Keywords: lower solution
zbMATH Keywords: extremal solution
MaRDI profile type: Publication
full work available at URL: s10957-004-5718-z
OpenAlex ID: W1973329837
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DOI: 10.1007/S10957-004-5718-Z
description: scientific article; zbMATH DE number 2154316