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Keywords:
homogenization; $G$-convergence; multiscale convergence; parabolic; asymptotic expansion
homogenization; $G$-convergence; multiscale convergence; parabolic; asymptotic expansion
Summary:
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.
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