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 ${mathbb R}^N$, 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 $lim_{varepsilono 0}{r_varepsilon/varepsilon}=0$ with nonzero-average data.

Keywords

• Diffusion equation
• composite material
• asymptotic behavior
• $H^0$-convergence.