Homogenization of linear parabolic equations with three spatial and three temporal scales for certain matchings between the microscopic scales
In this paper we establish compactness results of multiscale and very weak multiscale type for sequences bounded in $L^2(0,T;H_0^1(\Omega))$, fulfilling a certain condition. We apply the results in the homogenization of the parabolic partial differential equation $\varepsilon^p\partial_tu_{\varepsil...
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| Autores principales: | , |
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| Formato: | article |
| Lenguaje: | EN |
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Institute of Mathematics of the Czech Academy of Science
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/901588ce3f1340a2a6a03ac519dd46bb |
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| Sumario: | In this paper we establish compactness results of multiscale and very weak multiscale type for sequences bounded in $L^2(0,T;H_0^1(\Omega))$, fulfilling a certain condition. We apply the results in the homogenization of the parabolic partial differential equation $\varepsilon^p\partial_tu_{\varepsilon}(x,t) -\nabla\cdot( a( x\varepsilon^{-1} ,x\varepsilon^{-2},t\varepsilon^{-q},t\varepsilon^{-r}) \nabla u_{\varepsilon}(x,t) ) = f(x,t) $, where $0<p<q<r$. The homogenization result reveals two special phenomena, namely that the homogenized problem is elliptic and that the matching for which the local problem is parabolic is shifted by $p$, compared to the standard matching that gives rise to local parabolic problems. |
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