Global structure of steady-states to the full cross-diffusion limit in the Shigesada-Kawasaki-Teramoto model
Global structure of steady-states to the full cross-diffusion limit in the Shigesada-Kawasaki-Teramoto model
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DOI：
10.1016/j.jde.2022.06.002
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发表时间：
2021-06
影响因子：
2.4
通讯作者：
Kousuke Kuto
中科院分区：
文献类型：
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作者：
Kousuke Kuto
在文献[10]中，作者研究了Shigesada-Kawasaki-Teramoto模型在交叉扩散系数以相同的速率趋于无穷大时共存定态的渐近行为。结果，他证明了渐近行为可以用一个由半线性椭圆方程和积分约束组成的极限系统来表征。本文研究极限系统的解集。第一个主要结果利用Leray-Schauder度的拓扑方法给出了极限系统非常数解存在/不存在的充分条件。第二个主要结果通过对加权时间映射和非局部约束的分析，给出了一维极限系统非常数解的分岔图。
In a previous paper [10], the author studied the asymptotic behavior of coexistence steady-states to the Shigesada-Kawasaki-Teramoto model as both cross-diffusion coefficients tend to infinity at the same rate. As a result, he proved that the asymptotic behavior can be characterized by a limiting system that consists of a semilinear elliptic equation and an integral constraint. This paper studies the set of solutions of the limiting system. The first main result gives sufficient conditions for the existence/nonexistence of nonconstant solutions to the limiting system by a topological approach using the Leray-Schauder degree. The second main result exhibits a bifurcation diagram of nonconstant solutions to the one-dimensional limiting system by analysis of a weighted time-map and a nonlocal constraint.