Non-autonomous attractors for singularly perturbed parabolic equations on R n

We study the asymptotic behavior of solutions of a class of singularly perturbed non-autonomous parabolic equations defined on R n with unbounded external terms. We first prove the existence of a pullback attractor for the perturbed equation in L 2 ( R n ) and then establish the upper semicontinuity...

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Bibliographic Details
Published inNonlinear analysis Vol. 73; no. 10; pp. 3336 - 3347
Main Authors Gabert, Kasimir, Wang, Bixiang
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 15.11.2010
Subjects
Asymptotic compactness
Non-autonomous equation
Pullback attractor
secondary
Non-autonomous equation
Asymptotic compactness
primary
Pullback attractor
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Summary:We study the asymptotic behavior of solutions of a class of singularly perturbed non-autonomous parabolic equations defined on R n with unbounded external terms. We first prove the existence of a pullback attractor for the perturbed equation in L 2 ( R n ) and then establish the upper semicontinuity of these attractors as small perturbations approach zero. The uniform estimates on the tails of solutions are used to overcome the difficulty caused by the non-compactness of Sobolev embeddings on unbounded domains.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2010.07.014