Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 15, pp. 1-11.

Title: A diffusion equation for composite materials

Author: Mohamed El Hajji (Universite de  Rouen, France) 
  
Abstract: 
 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 ${\mathbb R}^N$, 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; $H^0$-convergence.