Estimates on the dimension of a global attractor for a semilinear dissipative wave equation on R-N

Karachalios, NI; Stavrakakis, NM

dc.contributor.author	Karachalios, NI	en
dc.contributor.author	Stavrakakis, NM	en
dc.date.accessioned	2014-03-01T01:52:05Z
dc.date.available	2014-03-01T01:52:05Z
dc.date.issued	2002	en
dc.identifier.issn	1078-0947	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/26552
dc.subject	dynamical systems	en
dc.subject	attractors	en
dc.subject	hyperbolic equations	en
dc.subject	unbounded domains	en
dc.subject	generalized Sobolev spaces	en
dc.subject	Hausdorff dimension	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	EVOLUTION-EQUATIONS	en
dc.subject.other	UNBOUNDED-DOMAINS	en
dc.subject.other	NONEXISTENCE	en
dc.subject.other	EXISTENCE	en
dc.title	Estimates on the dimension of a global attractor for a semilinear dissipative wave equation on R-N	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2002	en
heal.abstract	We discuss estimates of the Hausdorff and fractal dimension of a global attractor for the semilinear wave equation u(tt) + deltau(t) - phi(x)Deltau + lambdaf(u) = eta(x), x is an element of R-N, t greater than or equal to 0, with the initial conditions u(x, 0) = u(0) (x) and ut (x, 0) = u(1) (x), where N greater than or equal to 3, delta > 0 and (phi(x))(-1) := g(x) lies in L-N/2(RN) boolean AND L-infinity(RN). The energy space chi(0) = D-1,D-2(R-N) x L-g(2)(R-N) is introduced, to overcome the difficulties related with the non-compactness of operators, which arise in unbounded domains. The estimates on the Hausdorff dimension are in terms of given parameters, due to an asymptotic estimate for the eigenvalues mu of the eigenvalue problem -phi(x)Deltau = muu, x is an element of R-N.	en
heal.publisher	AMER INST MATHEMATICAL SCIENCES	en
heal.journalName	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS	en
dc.identifier.isi	ISI:000178082600009	en
dc.identifier.volume	8	en
dc.identifier.issue	4	en
dc.identifier.spage	939	en
dc.identifier.epage	951	en