Homogenization of some parabolic operators with several time scales

The main focus in this paper is on homogenization of the parabolic problem ∂ _t uɛ − ∇ · (a(x/ɛ,t/ɛ,t/ɛ ^r )∇u ^ɛ ) = f. Under certain assumptions on a, there exists a G-limit b, which we characterize by means of multiscale techniques for r > 0, r ≠ 1. Also, an interpretation of asymptotic expansions in the context of two-scale convergence is made.