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Homogenization of Linear Parabolic Equations with a Certain Resonant Matching Between Rapid Spatial and Temporal Oscillations in Periodically Perforated Domains

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Abstract

In this article, we study homogenization of a parabolic linear problem governed by a coefficient matrix with rapid spatial and temporal oscillations in periodically perforated domains with homogeneous Neumann data on the boundary of the holes. We prove results adapted to the problem for characterization of multiscale limits for gradients and very weak multiscale convergence.

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  1. Department of Mathematics and Science Education, Mid Sweden University, S-83125, Östersund, Sweden

    Tatiana Lobkova

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  1. Tatiana Lobkova
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Lobkova, T. Homogenization of Linear Parabolic Equations with a Certain Resonant Matching Between Rapid Spatial and Temporal Oscillations in Periodically Perforated Domains. Acta Math. Appl. Sin. Engl. Ser. 35, 340–358 (2019). https://doi.org/10.1007/s10255-019-0810-1

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  • DOI: https://doi.org/10.1007/s10255-019-0810-1

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