Homogenization of Acoustic Equations for a Partially Perforated Elastic Material with Slightly Viscous Fluid

Abstract

In this paper a mathematical model describing small oscillations of a heterogeneous medium is considered. The medium consists of a partially perforated elastic material and a slightly viscous compressible fluid filling the pores. For the given model the corresponding homogenized problem is constructed by using the two-scale convergence method. The boundary conditions connecting equations of the homogenized model on the boundary between the continuous elastic material and the porous elastic material with fluid are found.