# Asymptotic Behavior of Nonlinear Systems in Varying Domains with Boundary Conditions on Varying Sets

#### Abstract

Abstract. For a fixed bounded open set Ω ⊂ R , a sequence of open sets Ωn ⊂ Ω and a sequence of sets Γn ⊂ ∂Ω ∩ ∂Ωn, we study the asymptotic behavior of the solution of a nonlinear elliptic system posed on Ωn, satisfying Neumann boundary conditions on Γn and Dirichlet boundary conditions on ∂Ωn \ Γn. We obtain a representation of the limit problem which is stable by homogenization and we prove that this representation depends on Ωn and Γn locally.

### Cite this paper

@inproceedings{CalvoJurado2009AsymptoticBO, title={Asymptotic Behavior of Nonlinear Systems in Varying Domains with Boundary Conditions on Varying Sets}, author={Carmen Calvo-Jurado and Juan Casado-Dı́az and Manuel Luna-Laynez}, year={2009} }