Homogenization in heterogeneous media modeled by the Laplace-Beltrami operator

The study of thermal, mechanical and electrical properties of composite materials plays an increasingly important role in material sciences because of their wide spectrum of applica- tions, for instance, in industrial processes, biomathematics, medical diagnosis. In this talk, we discuss some models which describe the thermal diffusivity or the electrical conductivity in a composite medium with a nely mixed periodic structure, assuming that the microstructure of the materials under consideration is made by two different diffusive or conductive regions separated by an active interface ([1, 2, 3]). From the mathematical point of view, these models are described by a system of parabolic or elliptic equations in the two bulk phases, coupled through the interface by means of an equation involving the Laplace-Beltrami operator. Since the characteristic length of the microstructure is very small, we are led to study the limit behaviour of the medium, when the spatial period of the medium goes to zero, in order to produce the so-called \macroscopic" or \homogenized" models.