一类带小参数交错扩散竞争方程组行波解的存在性

The Existence of Traveling Wave for a Cross-Diffusion Competition System with Small Parameter

本文研究一类由著名学者Shigesada等人提出的带小参数交错扩散竞争系统行波解的存在性.在假设b_1/b_2<a_1/a_2<c_1/c_2的前提下,利用几何奇异摄动方法,证明当交错扩散系数γ_2充分大时系统存在连接两半平凡平衡点(0,a_2/c_2)和(a_1/b_1,0)的带边界层的行波解,且具有局部唯一的慢波速.

This paper is concerned with the existence of traveling wave for a cross-diffusion competition system with small parameter proposed by famous experts Shigesada et al. Under the assumption b_1/b_2a_1/a_2c_1/c_2, by using the geometric singular perturbation method, we can prove that there exists traveling wave with layer and with a local unique slow wave speed connecting two semi-trivial steady-states （0,a_2/c_2） and （a_1/b_1,0）,where the coefficient of the cross-diffusion γ_2 is large enough.