# 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

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topCalvo-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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