Semilinear parabolic problems in thin domains with a highly oscillatory boundary

Autor(es)

Arrieta, Jose M. ^[1] ; Carvalho, Alexandre N. ^[2] ; Pereira, Marcone C. ^[3] ; Silva, Ricardo P. ^[4]

Afiliação do(s) autor(es)

^[1] Univ Complutense Madrid, Dept Matemat Aplicada, E-28040 Madrid - Spain

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil

^[3] Univ Sao Paulo, Escola Artes Ciencias & Humanidades, BR-03828000 Sao Paulo, SP - Brazil

^[4] Univ Estadual Paulista, Inst Geociencias & Ciencias Exatas, BR-13506900 Rio Claro, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 74, n. 15, p. 5111-5132, 2011.
• Citações Web of Science: 32

Resumo

In this paper, we study the behavior of the solutions of nonlinear parabolic problems posed in a domain that degenerates into a line segment (thin domain) which has an oscillating boundary. We combine methods from linear homogenization theory for reticulated structures and from the theory on nonlinear dynamics of dissipative systems to obtain the limit problem for the elliptic and parabolic problems and analyze the convergence properties of the solutions and attractors of the evolutionary equations. (C) 2011 Elsevier Ltd. All rights reserved. (AU)

• Processo FAPESP: 08/53094-4 - Sistemas dinâmicos em espaços de dimensão infinita sob perturbações
• Beneficiário: Alexandre Nolasco de Carvalho
• Modalidade de apoio: Bolsas no Exterior - Pesquisa
• Processo FAPESP: 10/18790-0 - Comportamento assintótico e geométrico de equações diferenciais parciais
• Beneficiário: Marcone Corrêa Pereira
• Modalidade de apoio: Auxílio à Pesquisa - Regular