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Asymptotic behavior of nonlinear systemsin varying domains with boundary conditions on varying sets

Published online by Cambridge University Press:  23 January 2009

Carmen Calvo-Jurado ,
Juan Casado-Díaz  and
Manuel Luna-Laynez
Carmen Calvo-Jurado
Affiliation:
Dpto. de Matemáticas, Escuela Politécnica, Avenida de la Universidad s/n, 10071 Cáceres, Spain. ccalvo@unex.es
Juan Casado-Díaz
Affiliation:
Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Fac. de Matemáticas, C. Tarfia s/n, 41012 Sevilla, Spain. jcasadod@us.es; mllaynez@us.es
Manuel Luna-Laynez
Affiliation:
Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Fac. de Matemáticas, C. Tarfia s/n, 41012 Sevilla, Spain. jcasadod@us.es; mllaynez@us.es
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Abstract


For a fixed bounded open set $\Omega\subset\mathbb{R}^N$, a sequence of open sets $\Omega_n\subset\Omega$ and a sequence of sets $\Gamma_n\subset\partial\Omega\cap\partial\Omega_n$, we study the asymptotic behavior of the solution of a nonlinear elliptic system posed on $\Omega_n$, satisfying Neumann boundary conditions on $\Gamma_n$ and Dirichlet boundary conditions on $\partial\Omega_n\setminus \Gamma_n$. We obtain a representation of the limit problem which is stable by homogenization and we prove that this representation depends on $\Omega_n$ and $\Gamma_n$ locally.


Keywords

Homogenizationvarying domainsnonlinear problems
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 1 , January 2009 , pp. 49 - 67
Copyright
© EDP Sciences, SMAI, 2008

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