Multiscale convergence and reiterated homogenization of parabolic problems
Anders Holmbom, Nils Svanstedt, Niklas Wellander · Applications of Mathematics · 2005
Reiterated homogenization is studied for divergence structure parabolic problems of the form ∂ u ɛ/∂t−div (a(x,x/ɛ,x/ɛ2,t,t/ɛ k)∇u ɛ)=f. It is shown that under standard assumptions on the function a(x, y 1,y 2,t,τ) the sequence {u ɛ} 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)∇u)=f.