Large number asympotics for dispersed, non regular distributions of inclusions in a fluid

Abstract

We shall describe the large number asymtpotics for systems consisting in a fluid surrounding a non regular distributions of inclusions. The fluid satisfies a given boundary (or initial-boundary) value problem (involving a second order operator of divergence form) in a perforated domain and the holes in the domain are occupied by the inclusions; fluid and inclusions are coupled by the boundary conditions only. These systems are meant as models at some "microscopic" scale for describing, in a suitable asymptotics, the behaviour at a macroscopic level of composite media. We shall give a general overview of the results about the homogenized limit of such a kind of systems obtained in previous works (performed in collaboration with L. Desvillettes and F.Golse) under a different perspective. In particular we shall describe the homogenized limit in the frame of the potential theory, generalising those results with respect to the dimension of the physical space and the shape of the inclusions