Asymptotic behavior of nonlinear systems in varying domains with boundary conditions on varying sets

Calvo-Jurado, Carmen; Casado-Díaz, Juan; Luna-Laynez, Manuel

ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 1, pp. 49-67

For a fixed bounded open set $\Omega \subset {ℝ}^N$, 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.

Classification : 35B40
Keywords: homogenization, varying domains, nonlinear problems

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