Reiterated homogenization and G-convergence for some sequences of monotone operators

University dissertation from Östersund : Mittuniversitetet

Abstract: In this thesis, the main focus is on G-convergence and homogenization of monotone parabolic equations with multiple scales. This kind of equation is examined with respect to existence and uniqueness of the solution, in view of the properties of some monotone operators. We discuss the notion of G-convergence for elliptic and parabolic equations and prove that there exists a G-limit for the monotone parabolic multiple scale case. We consider two-scale convergence and the homogenization method based on this notion, and also its generalization to multiple scales, so-called reiterated homogenization. Moreover, we extend this type of convergence and prove a compactness result for a case in which there may also be oscillations in time. Finally, we apply these results for the homogenization of monotone parabolic equations with multiple scales.

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