反应交叉扩散方程组的精确行波解
Exact Propagating Wave Solutions in Reaction Cross-Diffusion System
摘要：
具有交叉扩散项的反应扩散系统除了或代替通常的自扩散项，表现出有趣的特征，这些特征激发了对它们的进一步研究。本文的目的是设计一个具有传播锋形式的精确解的玩具反应-交叉扩散模型。我们提出了一个极小模型，其中涉及两个物种的交叉扩散，其中一个由线性方程和其他具有多项式动力学项。我们分类得到的精确传播前的解决方案。其中一些具有Fisher-KPP锋和ZFK-Nagumo锋的某些特征。
英文摘要：
Reaction-diffusion systems with cross-diffusion terms in addition to, or instead of, the usual self-diffusion demonstrate interesting features which motivate their further study. The present work is aimed at designing a toy reaction-cross-diffusion model with exact solutions in the form of propagating fronts. We propose a minimal model of this kind which involves two species linked by cross-diffusion, one of which governed by a linear equation and the other having a polynomial kinetic term. We classify the resulting exact propagating front solutions. Some of them have some features of the Fisher-KPP fronts and some features of the ZFK-Nagumo fronts.
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