Multivalued perturbations of subdifferential type evolution equations in Hilbert spaces

Kravvaritis, D; Papageorgiou, NS

dc.contributor.author	Kravvaritis, D	en
dc.contributor.author	Papageorgiou, NS	en
dc.date.accessioned	2014-03-01T01:07:12Z
dc.date.available	2014-03-01T01:07:12Z
dc.date.issued	1988	en
dc.identifier.issn	00220396	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/9853
dc.subject	Evolution Equation	en
dc.subject	Hilbert Space	en
dc.title	Multivalued perturbations of subdifferential type evolution equations in Hilbert spaces	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/0022-0396(88)90073-3	en
heal.identifier.secondary	http://dx.doi.org/10.1016/0022-0396(88)90073-3	en
heal.publicationDate	1988	en
heal.abstract	In this paper we study the multivalued evolution equation - x ̇(t)ε{lunate}∂θ{symbol}(x(t)) + F(t, x(t)), x(0) = x0, where θ{symbol}: X → R ̄ is a proper, convex, lower semicontinuous (l.s.c.) function, F(·, ·) is a multivalued perturbation, and X is an infinite dimensional, separable Hilbert space. We have an existence result for F(·, ·) being nonconvex valued, and another for F(·, ·) being convex valued but not closed valued. When θ{symbol} = δK = indicator function of a compact, convex set K, we obtain some extensions of earlier results by Moreau and Henry. Then using the Kuratowski-Mosco convergence of sets and the τ-convergence of functions, we prove a well posedness result for the evolution inclusion we are studying. Also we consider a random version of it and prove the existence of a random solution. Finally we present applications to problems in partial differential equations. © 1988.	en
heal.journalName	Journal of Differential Equations	en
dc.identifier.doi	10.1016/0022-0396(88)90073-3	en
dc.identifier.volume	76	en
dc.identifier.issue	2	en
dc.identifier.spage	238	en
dc.identifier.epage	255	en