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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.

acta mathematicae applicatae sinica

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