A. Jüngel, M. Ptashnyk:

"Homogenization of degenerate cross-diffusion systems";

in: "ASC Report 27/2018", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2018, ISBN: 978-3-902627-11-7, 1 - 30.

Two-scale homogenization limits of parabolic cross-diﬀusion systems in a heterogeneous medium with no-ﬂux boundary conditions are proved. The heterogeneity of the medium is reﬂected in the diﬀusion coeﬃcients or by the perforated domain. The diﬀusion matrix is of degenerate type and may be neither symmetric nor positive semi-deﬁnite, but the diﬀusion system is assumed to satisfy an entropy structure. Uniform estimates are derived from the entropy production inequality. New estimates on the equicontinuity with respect to the time variable ensure the strong convergence of a sequence of solutions to the microscopic problems deﬁned in perforated domains.

Periodic homogenization, strongly coupled parabolic systems, two-scale convergence, perforated domain, entropy method

http://www.asc.tuwien.ac.at/preprint/2018/asc27x2018.pdf

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