Article contents
Asymptotic behavior of nonlinear systemsin varying domains with boundary conditions on varying sets
Published online by Cambridge University Press: 23 January 2009
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 theasymptotic behavior of the solution of a nonlinear ellipticsystem posed on $\Omega_n$
, satisfying Neumann boundary conditionson $\Gamma_n$
and Dirichlet boundary conditions on $\partial\Omega_n\setminus \Gamma_n$
. We obtain a representationof the limit problem which is stable by homogenization and weprove that this representation depends on $\Omega_n$
and $\Gamma_n$
locally.
- 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
References
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