A Diffusion Equation for Composite Materials
El Hajji, Mohamed
Southwest Texas State University, Department of Mathematics
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.
Diffusion equation, Composite material, Asymptotic behavior, H0-convergence
El Hajji, M. (2000). A diffusion equation for composite materials. <i>Electronic Journal of Differential Equations, 2000</i>(15), pp. 1-11.