Semilinear parabolic problems in thin domains with a highly oscillatory boundary期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Semilinear parabolic problems in thin domains with a highly oscillatory boundary

Authors:	José M. Arrieta,Marcone C. Pereira

Affiliation:	^a Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain ^b Instituto de Ciências Matemáticas e de Computaçao, Universidade de São Paulo-Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos SP, Brazil ^c Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Rua Arlindo Béttio, 03828-000 São Paulo SP, Brazil ^d Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista, 13506-900 Rio Claro SP, Brazil

Abstract:	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.

Keywords:	Thin domains Dissipative parabolic equations Global attractors Upper semicontinuity Lower semicontinuity Homogenization
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