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

Author： Calvo-Jurado Carmen   Casado-Díaz Juan   Luna-Laynez Manuel  

Publisher： Edp Sciences

E-ISSN： 1262-3377|15|1|49-67

ISSN： 1292-8119

Source： ESAIM: Control, Optimisation and Calculus of Variations, Vol.15, Iss.1, 2009-01, pp. : 49-67

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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 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.


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