Multiscale stochastic homogenization of monotone operators

Nils Svanstedt

doi:10.3934/nhm.2007.2.181

Article Contents

2007, Volume 2, Issue 1: 181-192. Doi: 10.3934/nhm.2007.2.181

This issue Previous Article Conservation laws with discontinuous flux Next Article

Multiscale stochastic homogenization of monotone operators

Nils Svanstedt^1,

1.
Department of Computational Mathematics, Chalmers University, SE-412 96 Göteborg

Received: January 31, 2006

Revised: August 31, 2006

Published: February 2007

Abstract Related Papers Cited by

Abstract

Multiscale stochastic homogenization is studied for divergence structure parabolic problems. More specifically we consider the asymptotic behaviour of a sequence of realizations of the form
$\frac{\partial u^\omega_\varepsilon}{\partial t}- $div$(a(T_1(\frac{x}{\varepsilon_1})\omega_1, T_2(\frac{x}{\varepsilon_2})\omega_2 ,t, D u^\omega_\varepsilon))=f.$
It is shown, under certain structure assumptions on the random map $a(\omega_1,\omega_2,t,\xi)$, that the sequence $\{u^\omega_\e}$ of solutions converges weakly in $ L^p(0,T;W^{1,p}_0(\Omega))$ to the solution $u$ of the homogenized problem $ \frac{\partial u}{\partial t} - $div$( b( t,D u )) = f$.

Keywords:

Mathematics Subject Classification: 35B27, 35B40.

Citation:

Article Metrics

HTML views() PDF downloads(172) Cited by(0)

Multiscale stochastic homogenization of monotone operators

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Multiscale stochastic homogenization of monotone operators

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content