Multiscale convergence and reiterated homogenization of parabolic problems

• DOI: 10.1007/s10492-005-0009-z
• Publication Date: 2005-03-25T00:31:32Z
• Authors: Anders Holmbom; Nils Svanstedt; Niklas Wellander
• Keywords: 0101 mathematics; 01 natural sciences

Reiterated homogenization is studied for divergence structure parabolic problems of the form ∂ uɛ/∂t−div (a(x,x/ɛ,x/ɛ2,t,t/ɛ k)∇uɛ)=f. It is shown that under standard assumptions on the function a(x, y1,y2,t,τ) the sequence {uɛ} of solutions converges weakly in L2 (0,T; H01(Ω)) to the solution u of the homogenized problem ∂u/∂t− div(b(x,t)∇u)=f.