Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 74, Issue 15, Pages 5111-5132Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2011.05.006
Keywords
Thin domains; Dissipative parabolic equations; Global attractors; Upper semicontinuity; Lower semicontinuity; Homogenization
Categories
Funding
- MICINN, Spain [MTM2009-07540, PHB2006-003 PC, PR2009-0027, GR58/08, GR35/10-A, 920894]
- CNPq [305447/2005-0, 451761/2008-1, 305210/2008-4]
- CAPES/DGU [267/2008]
- FAPESP, Brazil [2008/53094-4, 2010/18790-0]
- Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) [10/18790-0] Funding Source: FAPESP
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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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