When do cross-diffusion systems have an entropy structure?
When do cross-diffusion systems have an entropy structure?
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DOI：
10.1016/j.jde.2020.12.037
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发表时间：
2019-08
影响因子：
2.4
通讯作者：
Xiuqing Chen;A. Jüngel
中科院分区：
文献类型：
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作者：
Xiuqing Chen;A. Jüngel
本文基于矩阵分解的结果，给出了一类具有扩散矩阵A（u）的交叉扩散系统存在熵结构的充要条件.熵结构在分析这类方程时很重要，因为A（u）通常既不是对称的，也不是正定的。特别地，A（u）对所有u的正规椭圆性和昂萨格矩阵的对称性意味着它的正定性，因此是熵结构。如果A是常数或常数直到非线性扰动，熵结构的存在等价于A的正常椭圆性。结果被应用到物理学和生物学的各种例子。最后证明了Shigesada，川崎和Teramoto的n种群模型的正态椭圆性.
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.