When do cross-diffusion systems have an entropy structure?

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:278

Article

Chen, Xiuqing¹  Juengel, Ansgar² 

[1] Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai 519082, Guangdong, Peoples R China

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

关键词: Cross diffusion;    Normal ellipticity;    Matrix factorization;    Keller-Segel system;    Population model;    Fluid mixtures;   

DOI  :  10.1016/j.jde.2020.12.037

来源: Elsevier

【 摘 要 】

In this note, necessary and sufficient conditions for the existence of an entropy structure for certain classes of cross-diffusion systems with diffusion matrix A (u) are given, based on results from matrix factorization. The entropy structure is important in the analysis for such equations since A(u) is typically neither symmetric nor positive definite. In particular, the normal ellipticity of A(u) for all u and the symmetry of the Onsager matrix implies its positive definiteness and hence an entropy structure. If A is constant or constant up to nonlinear perturbations, the existence of an entropy structure is equivalent to the normal ellipticity of A. The results are applied to various examples from physics and biology. Finally, the normal ellipticity of the n-species population model of Shigesada, Kawasaki, and Teramoto is proved. (C) 2021 The Author(s). Published by Elsevier Inc.

【 授权许可】

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