Semilinear parabolic problems in thin domains with a highly oscillatory boundary
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Data
2011-10-01
Autores
Arrieta, Jose M.
Carvalho, Alexandre N.
Pereira, Marcone C.
Silva, Ricardo P. [UNESP]
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Pergamon-Elsevier B.V. Ltd
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.
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Thin domains, Dissipative parabolic equations, Global attractors, Upper semicontinuity, Lower semicontinuity, Homogenization
Como citar
Nonlinear Analysis-theory Methods & Applications. Oxford: Pergamon-Elsevier B.V. Ltd, v. 74, n. 15, p. 5111-5132, 2011.