Homogenization of linear parabolic equations with three spatial and three temporal scales for certain matchings between the microscopic scales
Tatiana Danielsson, Pernilla Johnsen · Mathematica Bohemica · 2021
In this paper we establish compactness results of multiscale and very weak multiscale type for sequences bounded in $L^{2}(0,T;H_{0}^{1}(Ω))$, fulfilling a certain condition. We apply the results in the homogenization of the parabolic partial differential equation $\varepsilon ^{p}\partial_{t}u_{\varepsilon }\left( x,t\right) - abla \cdot \left( a\left( x/\varepsilon ,x/\varepsilon ^{2},t/\varepsilon^{q},t/\varepsilon ^{r}\right) abla u_{\varepsilon }\left( x,t\right)\right) = f\left( x,t\right) $, where $0