Homogenization of the Stefan Problem and Application to Magnetic Composite Media
A. Bossavit, Alain Damlamian · IMA Journal of Applied Mathematics · 1981
The theory of homogenization (Bensoussan, Lions & Papanicolaou, 1978) shows that uε, the solution of the diffusion equation [with k(y) periodic in the space-variable y and q = cu a linear function of u] has a weak limit u for ε = 0. This theory allows one to compute, for a given k, the conductivity tensor of an anisotropic but homogeneous medium in which, for unchanged initial and boundary conditions, u is the solution of the diffusion equation. We examine here the case where the relation between q and u is given by a maximal monotone graph (i.e. the Stefan problem), depending on the space variable in the same manner as k. Applications to eddy-current problems in magnetic composite media (steel cables, laminations) are suggested. A numerical example is given.