Second order nonlinear evolution inclusions I: Existence and relaxation results

Papageorgiou, NS; Yannakakis, N

dc.contributor.author	Papageorgiou, NS	en
dc.contributor.author	Yannakakis, N	en
dc.date.accessioned	2014-03-01T01:23:03Z
dc.date.available	2014-03-01T01:23:03Z
dc.date.issued	2005	en
dc.identifier.issn	1439-8516	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16787
dc.subject	Coercive operator	en
dc.subject	Compact embedding	en
dc.subject	Evolution triple	en
dc.subject	Extremal solutions	en
dc.subject	Integration by parts formula	en
dc.subject	Lpseudomonotonicity	en
dc.subject	Pseudomonotone and demicontinuous operator	en
dc.subject	Solution set	en
dc.subject	Upper semicontinuous and lower semicontinuous multifunction	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	GENERAL BANACH-SPACES	en
dc.subject.other	DIFFERENTIAL-INCLUSIONS	en
dc.subject.other	NONMONOTONE	en
dc.subject.other	LINES	en
dc.title	Second order nonlinear evolution inclusions I: Existence and relaxation results	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s10114-004-0508-y	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s10114-004-0508-y	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x(t) and x(t). In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C1(T,H). Also we examine the lsc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C1(T,H) to the solutions of the original convex problem (strong relaxation). An example of a nonlinear hyperbolic optimal control problem is also discussed. © Springer-Verlag 2005.	en
heal.publisher	SPRINGER HEIDELBERG	en
heal.journalName	Acta Mathematica Sinica, English Series	en
dc.identifier.doi	10.1007/s10114-004-0508-y	en
dc.identifier.isi	ISI:000232720700002	en
dc.identifier.volume	21	en
dc.identifier.issue	5	en
dc.identifier.spage	977	en
dc.identifier.epage	996	en