Abstract: This talk addresses the issue of homogenization of linear divergence form parabolic operators in situations where no ergodicity and no scale separation in time or space are available .
We develop the method in  and consider divergence form linear parabolic operators in with coefficients. Actually, we can show that under a parabolic Cordes condition the first order time derivative and second order space derivatives are w.r.t harmonic coordinates (instead of in Euclidean coordinates). Therefore we can approximate the solution space in norm with a functional space of dimension . It follows that once we solved the equation at least -times, we can homogenize them both in time and space.
Similar idea can also be applied to acoustic wave equation .