A Diffusion Equation for Composite Materials

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 ℝN, with small holes whose sizes are measured by a number r∊. We examine the case when rε < εN/(N-2) with zero-average data around the holes, and the case when limε→0 rε/ε = 0 with nonzero-average data.