Multiscale convergence and reiterated homogenization of parabolic problems

Reiterated homogenization is studied for divergence structure parabolic problems of the form ∇ u ε/∇t-div (a(x,x/ε,x/ε 2,t,t/ε k)δu ε)=f. It is shown that under standard assumptions on the function a(x, y 1,y 2,t,τ) the sequence {u ε} of solutions converges weakly in L 2 (0,T; H 0 1 (Ω)) to the solution u of the homogenized problem ∇u/∇t- div(b(x,t)δu)=f. © 2005 Springer Science+Business Media, Inc.