Electron. J. Diff. Eqns., Vol. 2000(2000), No. 15, pp. 1-11.

A diffusion equation for composite materials

Mohamed El Hajji

In this article, we study the asymptotic behavior of solutions to the diffusion equation with non-homogeneous Neumann boundary conditions. This equation models a composite material that occupies a perforated domain, in ${\Bbb R}^N$, with small holes whose sizes are measured by a number $r_\varepsilon$. We examine the case when $r_\varepsilon$< $\varepsilon^{N/(N-2)}$ with zero-average data around the holes, and the case when $\lim_{\varepsilon\to 0}{r_\varepsilon/\varepsilon}=0$ with nonzero-average data.

Submitted October 14, 1999. Published February 22, 2000.
Math Subject Classifications: 31C40, 31C45, 60J50, 31C35, 31B35.
Key Words: Diffusion equation, composite material, asymptotic behavior, H0-convergence.

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Mohamed El Hajji
Universite de Rouen, UFR des Sciences
UPRES-A 60 85 (Labo de Math.)
76821 Mont Saint Aignan, France
e-mail address: Mohamed.Elhajji@univ-rouen.fr

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