Geodesic
Homogenization of some parabolic operators with several time scales
Applications of Mathematics, Tome 52 (2007) no. 5, pp. 431-446.

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The main focus in this paper is on homogenization of the parabolic problem $ \partial _{t}u^{\varepsilon }-\nabla \cdot ( a( {x}/{\varepsilon },{t}/{\varepsilon }, {t}/{\varepsilon ^{r}})\nabla u^{\varepsilon }) =f$. Under certain assumptions on $a$, there exists a $G$-limit $b$, which we characterize by means of multiscale techniques for $r>0$, $r\ne 1$. Also, an interpretation of asymptotic expansions in the context of two-scale convergence is made.
DOI : 10.1007/s10492-007-0025-2
Classification : 35B27, 35K20
Keywords: homogenization; $G$-convergence; multiscale convergence; parabolic; asymptotic expansion 
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Flodén, Liselott; Olsson, Marianne. Homogenization of some parabolic operators with several time scales. Applications of Mathematics, Tome 52 (2007) no. 5, pp. 431-446. doi : 10.1007/s10492-007-0025-2. http://geodesic.mathdoc.fr/articles/10.1007/s10492-007-0025-2/

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