Global attractor for the weakly damped driven Schrödinger equation in H2 (ℝ)

Karachalios, NI; Stavrakakis, NM

dc.contributor.author	Karachalios, NI	en
dc.contributor.author	Stavrakakis, NM	en
dc.date.accessioned	2014-03-01T01:17:56Z
dc.date.available	2014-03-01T01:17:56Z
dc.date.issued	2002	en
dc.identifier.issn	1021-9722	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14715
dc.subject	Attractors	en
dc.subject	Dynamical Systems	en
dc.subject	Schrödinger Equations	en
dc.subject	Unbounded Domains	en
dc.subject	Weighted Sobolev Spaces	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	CAUCHY-PROBLEM	en
dc.subject.other	EVOLUTION-EQUATIONS	en
dc.subject.other	EXISTENCE	en
dc.title	Global attractor for the weakly damped driven Schrödinger equation in H2 (ℝ)	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s00030-002-8132-y	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00030-002-8132-y	en
heal.language	English	en
heal.publicationDate	2002	en
heal.abstract	We discuss the asymptotic behaviour of the Schrödinger equation iut + ut + iαu - kσ(\|u\|2)u = f, x ε ℝ, t ≥ 0, α, k > 0 with the initial condition u(x, 0) = uo(x). We prove existence of a global attractor in H2(ℝ), by using a decomposition of the semigroup in weighted Sobolev spaces to overcome the noncompactness of the classical Sobolev embeddings. 2000 Mathematics Subject Classification: 35B40, 35L15, 35L70, 35L80, 58F39.	en
heal.publisher	BIRKHAUSER VERLAG AG	en
heal.journalName	Nonlinear Differential Equations and Applications	en
dc.identifier.doi	10.1007/s00030-002-8132-y	en
dc.identifier.isi	ISI:000177840000007	en
dc.identifier.volume	9	en
dc.identifier.issue	3	en
dc.identifier.spage	347	en
dc.identifier.epage	360	en