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Homogenization of some parabolic operators with several time scales. (English) Zbl 1164.35315

Summary: The main focus in this paper is on the 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 \(r>0\), \(r\neq 1\). Also, an interpretation of asymptotic expansions in the context of two-scale convergence is made.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
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References:

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