Geodesic
Homogenization of monotone parabolic problems with several temporal scales
Applications of Mathematics, Tome 57 (2012) no. 3, pp. 191-214 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.1007/s10492-012-0013-z
Classification : 35B05, 35B27, 35K59
Keywords: homogenization; $H$-convergence; multiscale convergence; parabolic; monotone; parabolic problem 
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Persson, Jens. Homogenization of monotone parabolic problems with several temporal scales. Applications of Mathematics, Tome 57 (2012) no. 3, pp. 191-214. doi: 10.1007/s10492-012-0013-z

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