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

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

ESAIM: Control, Optimisation and Calculus of Variations (2009)

  • Volume: 15, Issue: 1, page 49-67
  • ISSN: 1292-8119

Abstract

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


How to cite

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Calvo-Jurado, Carmen, Casado-Díaz, Juan, and Luna-Laynez, Manuel. "Asymptotic behavior of nonlinear systems in varying domains with boundary conditions on varying sets." ESAIM: Control, Optimisation and Calculus of Variations 15.1 (2009): 49-67. <http://eudml.org/doc/250570>.

@article{Calvo2009,
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 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.
},
author = {Calvo-Jurado, Carmen, Casado-Díaz, Juan, Luna-Laynez, Manuel},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Homogenization; varying domains; nonlinear problems; mixed boundary conditions},
language = {eng},
month = {1},
number = {1},
pages = {49-67},
publisher = {EDP Sciences},
title = {Asymptotic behavior of nonlinear systems in varying domains with boundary conditions on varying sets},
url = {http://eudml.org/doc/250570},
volume = {15},
year = {2009},
}

TY - JOUR
AU - Calvo-Jurado, Carmen
AU - Casado-Díaz, Juan
AU - Luna-Laynez, Manuel
TI - Asymptotic behavior of nonlinear systems in varying domains with boundary conditions on varying sets
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2009/1//
PB - EDP Sciences
VL - 15
IS - 1
SP - 49
EP - 67
AB - 
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 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.

LA - eng
KW - Homogenization; varying domains; nonlinear problems; mixed boundary conditions
UR - http://eudml.org/doc/250570
ER -

References

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