Maximum and minimum solutions for nonlinear parabolic problems with discontinuities

Kandilakis, DA; Papageorgiou, NS

dc.contributor.author	Kandilakis, DA	en
dc.contributor.author	Papageorgiou, NS	en
dc.date.accessioned	2014-03-01T01:13:53Z
dc.date.available	2014-03-01T01:13:53Z
dc.date.issued	1998	en
dc.identifier.issn	02534142	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/12768
dc.subject	Compact embedding	en
dc.subject	Evolution triple	en
dc.subject	Integration by parts	en
dc.subject	Lower solution	en
dc.subject	Regular cone	en
dc.subject	Sobolev space	en
dc.subject	Upper solution	en
dc.title	Maximum and minimum solutions for nonlinear parabolic problems with discontinuities	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/BF02841551	en
heal.identifier.secondary	http://dx.doi.org/10.1007/BF02841551	en
heal.publicationDate	1998	en
heal.abstract	In this paper we examine nonlinear parabolic problems with a discontinuous right hand side. Assuming the existence of an upper solution φ and a lower solution ψ such that ψ ≤ φ, we establish the existence of a maximum and a minimum solution in the order interval [ψ, φ]. Our approach does not consider the multivalued interpretation of the problem, but a weak one side ""Lipschitz"" condition on the discontinuous term. By employing a fixed point theorem for nondecreasing maps, we prove the existence of extremal solutions in [ψ, φ] for the original single valued version of the problem.	en
heal.journalName	Proceedings of the Indian Academy of Sciences: Mathematical Sciences	en
dc.identifier.doi	10.1007/BF02841551	en
dc.identifier.volume	108	en
dc.identifier.issue	2	en
dc.identifier.spage	179	en
dc.identifier.epage	187	en