Geodesic
Multiscale convergence and reiterated homogenization of parabolic problems
Applications of Mathematics, Tome 50 (2005) no. 2, pp. 131-151.

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Reiterated homogenization is studied for divergence structure parabolic problems of the form $\partial u_{\varepsilon }/\partial t - \div \bigl (a\bigl (x,x/\varepsilon ,x/\varepsilon ^2, t,t/\varepsilon ^{k}\bigr )\nabla u_{\varepsilon }\bigr )=f$. It is shown that under standard assumptions on the function $a(x,y_1,y_2,t,\tau )$ the sequence $\lbrace u_\epsilon \rbrace $ of solutions converges weakly in $L^2(0,T;H^1_0(\Omega ))$ to the solution $u$ of the homogenized problem $\partial u/\partial t -\div (b(x,t)\nabla u)=f$.
DOI : 10.1007/s10492-005-0009-z
Classification : 35B27, 35K20
Keywords: reiterated homogenization; multiscale convergence; parabolic equation 
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Holmbom, Anders; Svanstedt, Nils; Wellander, Niklas. Multiscale convergence and reiterated homogenization of parabolic problems. Applications of Mathematics, Tome 50 (2005) no. 2, pp. 131-151. doi : 10.1007/s10492-005-0009-z. http://geodesic.mathdoc.fr/articles/10.1007/s10492-005-0009-z/

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