Existence of a global attractor for semilinear dissipative wave equations on R N

Karachalios, NI; Stavrakakis, NM

dc.contributor.author	Karachalios, NI	en
dc.contributor.author	Stavrakakis, NM	en
dc.date.accessioned	2014-03-01T01:14:35Z
dc.date.available	2014-03-01T01:14:35Z
dc.date.issued	1999	en
dc.identifier.issn	0022-0396	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/13165
dc.subject	Attractors	en
dc.subject	Dynamical systems	en
dc.subject	Generalised Sobolev spaces	en
dc.subject	Hyperbolic equations	en
dc.subject	Nonlinear problems	en
dc.subject	Semigroups	en
dc.subject	Unbounded domains	en
dc.subject.classification	Mathematics	en
dc.subject.other	NONLINEAR HYPERBOLIC-EQUATIONS	en
dc.subject.other	EVOLUTION-EQUATIONS	en
dc.subject.other	NONEXISTENCE	en
dc.subject.other	DOMAINS	en
dc.subject.other	ENERGY	en
dc.title	Existence of a global attractor for semilinear dissipative wave equations on R N	en
heal.type	journalArticle	en
heal.identifier.primary	10.1006/jdeq.1999.3618	en
heal.identifier.secondary	http://dx.doi.org/10.1006/jdeq.1999.3618	en
heal.language	English	en
heal.publicationDate	1999	en
heal.abstract	We consider the semilinear hyperbolic problem u(tt) + delta u(t) - phi(x) Delta u + lambda f(u) = eta(x), x epsilon R-N, t > 0, with the initial conditions u(x,0) = u(0)(x) and u(t)(x, 0) = u(1)(x) in the case where N greater than or equal to 3 and (phi(x))(-1) : = g(x) lies in L-N/2(R-N). The energy space chi(0) = G(1,2)(R-N) x L-g(2) (R-N) is introduced, to overcome the difficulties related with the noncompactness of operators which arise in unbounded domains. We derive various estimates to show local existence of solutions and existence of a global attractor in chi(0). The compactness of the embedding L-1,L-2(R-N) subset of L-g(2)(R-N) is widely applied. (C) 1999 Academic Press.	en
heal.publisher	ACADEMIC PRESS INC	en
heal.journalName	Journal of Differential Equations	en
dc.identifier.doi	10.1006/jdeq.1999.3618	en
dc.identifier.isi	ISI:000082512100010	en
dc.identifier.volume	157	en
dc.identifier.issue	1	en
dc.identifier.spage	183	en
dc.identifier.epage	205	en