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Keywords:
homogenization; $H$-convergence; multiscale convergence; parabolic; monotone; parabolic problem
homogenization; $H$-convergence; multiscale convergence; parabolic; monotone; parabolic problem
Summary:
In this paper we homogenize monotone parabolic problems with two spatial scales and any number of temporal scales. Under the assumption that the spatial and temporal scales are well-separated in the sense explained in the paper, we show that there is an H-limit defined by at most four distinct sets of local problems corresponding to slow temporal oscillations, slow resonant spatial and temporal oscillations (the “slow” self-similar case), rapid temporal oscillations, and rapid resonant spatial and temporal oscillations (the ``rapid'' self-similar case), respectively.
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