Homogenization of some evolution problems in domains with small holes

Abstract

This article concerns the asymptotic behavior of the wave and heat equations in periodically perforated domains with small holes and Dirichlet conditions on the boundary of the holes. In the first part we extend to time-dependent functions the periodic unfolding method for domains with small holes introduced in [6]. Therein, the method was applied to the study of elliptic problems with oscillating coefficients in domains with small holes, recovering the homogenization result with a "strange term" originally obtained in [11] for the Laplacian. In the second part we obtain some homogenization results for the wave and heat equations with oscillating coefficients in domains with small holes. The results concerning the wave equation extend those obtained in [12] for the case where the elliptic part of the operator is the Laplacian.

Keywords

• Periodic unfolding method
• homogenization in perforated domains
• small holes
• wave equation
• heat equation