Homogenization of degenerate cross-diffusion systems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Jungel, Ansgar¹  Ptashnyk, Mariya² 

[1] Vienna Univ Technol, Inst Anal & Sci Comp, Wiedner Hauptst 8-10, A-1040 Vienna, Austria

[2] Heriot Watt Univ, Sch Math & Comp Sci, Dept Math, Edinburgh EH14 4AS, Midlothian, Scotland

关键词: Periodic homogenization;    Strongly coupled parabolic systems;    Two-scale convergence;    Perforated domain;    Entropy method;   

DOI  :  10.1016/j.jde.2019.05.036

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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