ASYMPTOTIC EXPANSIONS FOR HIGH-CONTRAST SCALAR AND VECTORIAL PDES

This paper is about solutions to PDEs in which the ratio between the largest and smallest values of the coefficient is very large. Such problems are referred to as high-contrast ones. A full asymptotic expansion of solutions to such high-contrast PDEs in terms of the high-contrast parameter is obtained for both scalar and vectorial cases. For the scalar case, we choose a diffusion process in a heterogeneous domain of finite conductivity with highly conducting particles, while for the vectorial case, we deal with the Lame system of linearized elasticity in the domain that contains almost rigid particles. Error estimates for asymptotic expansions are also derived.