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

DOI : https://doi.org/10.1051/cocv:2008021
Classification : 35B40
Mots clés : homogenization, varying domains, nonlinear problems
@article{COCV_2009__15_1_49_0,
title = {Asymptotic behavior of nonlinear systems in varying domains with boundary conditions on varying sets},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {49--67},
publisher = {EDP-Sciences},
volume = {15},
number = {1},
year = {2009},
doi = {10.1051/cocv:2008021},
zbl = {1170.35014},
mrnumber = {2488568},
language = {en},
url = {http://www.numdam.org/item/COCV_2009__15_1_49_0/}
}
Calvo-Jurado, Carmen; Casado-Díaz, Juan; Luna-Laynez, Manuel. Asymptotic behavior of nonlinear systems in varying domains with boundary conditions on varying sets. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 1, pp. 49-67. doi : 10.1051/cocv:2008021. http://www.numdam.org/item/COCV_2009__15_1_49_0/

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