Attractors for a Nonlinear Parabolic Problem with Terms Concentrating on the Boundary

Attractors for a Nonlinear Parabolic Problem with Terms Concentrating on the Boundary

Author Aragao, Gleiciane S. Autor UNIFESP Google Scholar
Pereira, Antonio L. Google Scholar
Pereira, Marcone C. Google Scholar
Institution Universidade Federal de São Paulo (UNIFESP)
Universidade de São Paulo (USP)
Abstract We analyze the dynamics of the flow generated by a nonlinear parabolic problem when some reaction and potential terms are concentrated in a neighborhood of the boundary. We assume that this neighborhood shrinks to the boundary as a parameter goes to zero. Also, we suppose that the inner boundary of this neighborhood presents a highly oscillatory behavior. Our main goal here is to show the continuity of the family of attractors with respect to . Indeed, we prove upper semicontinuity under the usual properties of regularity and dissipativeness and, assuming hyperbolicity of the equilibria, we also show the lower semicontinuity of the attractors at epsilon = 0.
Keywords Partial differential equations on infinite-dimensional spaces
Asymptotic behavior of solutions
Singular perturbations
Concentrating terms
Oscillatory behavior
Lower semicontinuity
Language English
Sponsor Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Grant number FAPESP: 2010/51829-7
FAPESP: 2008/55516-3
FAPESP: 2008/53094-4
FAPESP: 2010/18790-0
CNPq: 308696/2006-9
CNPq: 302847/2011-1
CNPq: 471210/2013-7
Date 2014-12-01
Published in Journal of Dynamics and Differential Equations. New York: Springer, v. 26, n. 4, p. 871-888, 2014.
ISSN 1040-7294 (Sherpa/Romeo, impact factor)
Publisher Springer
Extent 871-888
Access rights Closed access
Type Article
Web of Science ID WOS:000346171800003

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