Minimal solutions of nonlinear parabolic problems with unilateral constraints

Papageorgiou, NS; Papalini, F; Vercillo, S

dc.contributor.author	Papageorgiou, NS	en
dc.contributor.author	Papalini, F	en
dc.contributor.author	Vercillo, S	en
dc.date.accessioned	2014-03-01T01:13:12Z
dc.date.available	2014-03-01T01:13:12Z
dc.date.issued	1997	en
dc.identifier.issn	0362-1588	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/12348
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0004752773&partnerID=40&md5=e0fb65620430aed28982c7378fa06f0e	en
dc.subject	Arzela-Ascoli theorem	en
dc.subject	Minimum solution	en
dc.subject	Monotone operator	en
dc.subject	Subdifferential	en
dc.subject	Unilateral constraint	en
dc.subject	Upper solution	en
dc.subject	Variational inequality	en
dc.subject	Zorn's lemma	en
dc.subject.classification	Mathematics	en
dc.title	Minimal solutions of nonlinear parabolic problems with unilateral constraints	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1997	en
heal.abstract	In this paper we consider a class of nonlinear parabolic variational inequalities, we assume that it has an upper solution and we look for the minimal solution bounded above by the given upper soltuion. Our approach uses truncation and penalization techniques, which lead us to an auxiliary closely related problem. This is transformed to an equivalent abstract subdifferential evolution equation, which we solve. We then show that these solutions also solve the original variational inequality and they are bounded from above by the upper solution. Finally, an application of Zorn's lemma gives us the desired minimal solution.	en
heal.publisher	UNIV HOUSTON	en
heal.journalName	Houston Journal of Mathematics	en
dc.identifier.isi	ISI:000072032100018	en
dc.identifier.volume	23	en
dc.identifier.issue	1	en
dc.identifier.spage	189	en
dc.identifier.epage	201	en