Homogenization of a monotone problem in a domain with oscillating boundary

Blanchard, Dominique, Carbone, Luciano, and Gaudiello, Antonio. "Homogenization of a monotone problem in a domain with oscillating boundary." ESAIM: Mathematical Modelling and Numerical Analysis 33.5 (2010): 1057-1070. <http://eudml.org/doc/197595>.

@article{Blanchard2010,
abstract = { We study the asymptotic behaviour of the following nonlinear problem: $$\\{ \begin\{array\}\{ll\} -\{\rm div\}(a( Du\_h))+ \vert u\_h\vert^\{p-2\}u\_h =f \quad\hbox\{in \}\Omega\_h, a( Du\_h)\cdot\nu = 0 \quad\hbox\{on \}\partial\Omega\_h, \end\{array\} .$$ in a domain Ωh of $\mathbb\{R\}^n$ whose boundary ∂Ωh contains an oscillating part with respect to h when h tends to ∞. The oscillating boundary is defined by a set of cylinders with axis 0xn that are h-1-periodically distributed. We prove that the limit problem in the domain corresponding to the oscillating boundary identifies with a diffusion operator with respect to xn coupled with an algebraic problem for the limit fluxes. },
author = {Blanchard, Dominique, Carbone, Luciano, Gaudiello, Antonio},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Homogenization; nonlinear problem; oscillating boundary.; homogenization; oscillating boundary; nonlinear elliptic equation; Neumann boundary condition; asymptotic behaviour},
language = {eng},
month = {3},
number = {5},
pages = {1057-1070},
publisher = {EDP Sciences},
title = {Homogenization of a monotone problem in a domain with oscillating boundary},
url = {http://eudml.org/doc/197595},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Blanchard, Dominique
AU - Carbone, Luciano
AU - Gaudiello, Antonio
TI - Homogenization of a monotone problem in a domain with oscillating boundary
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 5
SP - 1057
EP - 1070
AB - We study the asymptotic behaviour of the following nonlinear problem: $$\{ \begin{array}{ll} -{\rm div}(a( Du_h))+ \vert u_h\vert^{p-2}u_h =f \quad\hbox{in }\Omega_h, a( Du_h)\cdot\nu = 0 \quad\hbox{on }\partial\Omega_h, \end{array} .$$ in a domain Ωh of $\mathbb{R}^n$ whose boundary ∂Ωh contains an oscillating part with respect to h when h tends to ∞. The oscillating boundary is defined by a set of cylinders with axis 0xn that are h-1-periodically distributed. We prove that the limit problem in the domain corresponding to the oscillating boundary identifies with a diffusion operator with respect to xn coupled with an algebraic problem for the limit fluxes.
LA - eng
KW - Homogenization; nonlinear problem; oscillating boundary.; homogenization; oscillating boundary; nonlinear elliptic equation; Neumann boundary condition; asymptotic behaviour
UR - http://eudml.org/doc/197595
ER -