Homogenization of degenerate cross-diffusion systems

Ansgar Jüngel, Mariya Ptashnyk

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2 Citations (Scopus)
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Abstract

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.

Original languageEnglish
Pages (from-to)5543-5575
Number of pages33
JournalJournal of Differential Equations
Volume267
Issue number9
Early online date4 Jun 2019
DOIs
Publication statusPublished - 15 Oct 2019

Keywords

  • Entropy method
  • Perforated domain
  • Periodic homogenization
  • Strongly coupled parabolic systems
  • Two-scale convergence

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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