Multiscale stochastic homogenization of convection-diffusion equations
Nils Svanstedt · Applications of Mathematics · 2008
Multiscale stochastic homogenization is studied for convection-diffusion problems. More specifically, we consider the asymptotic behaviour of a sequence of realizations of the form ∂u / ∂t+1 / ɛ 3 C(T 3(x/ɛ 3)ω 3) · ∇u − div(α(T 2(x/ɛ 2)ω 2, t) ∇u ) = f. It is shown, under certain structure assumptions on the random vector field C(ω 3) and the random map α(ω 1, ω 2, t), that the sequence {u } of solutions converges in the sense of G-convergence of parabolic operators to the solution u of the homogenized problem ∂u/∂t − div (B(t)∇u= f).