# Homogenization of a monotone problem in a domain with oscillating boundary

Dominique Blanchard; Luciano Carbone; Antonio Gaudiello

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 33, Issue: 5, page 1057-1070
- ISSN: 0764-583X

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topBlanchard, 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 -

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