Homogenization of the Stefan Problem and Application to Magnetic Composite Media

The theory of homogenization (Bensoussan, Lions & Papanicolaou,1978) shows that u, the solution of the diffusion equation [with k(y) periodic in the space-variable y and q = cu a linearfunction of u] has a weak limit u for = 0. This theory allowsone to compute, for a given k, the conductivity tensor of ananisotropic but homogeneous medium in which, for unchanged initialand boundary conditions, u is the solution of the diffusionequation. We examine here the case where the relation between q and uis given by a maximal monotone graph (i.e. the Stefan problem),depending on the space variable in the same manner as k. Applicationsto eddy-current problems in magnetic composite media (steelcables, laminations) are suggested. A numerical example is given.