Slow and fast minimal speed traveling waves of the FKPP equation with chemotaxis
Slow and fast minimal speed traveling waves of the FKPP equation with chemotaxis
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DOI：
10.1016/j.matpur.2022.09.004
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发表时间：
2021-02
期刊：
影响因子：
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通讯作者：
Christopher Henderson
中科院分区：
文献类型：
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作者：
Christopher Henderson
我们研究了一个具有非局部平流的Fisher-KPP(FKPP)方程的一般模型。这个模型的主要解释是描述了一个扩散和逻辑上不断增长的种群，这种种群也受到种内吸引或排斥的影响。对于特定的参数选择，这专门针对趋化性的Keller-Segel-Fisher方程。我们感兴趣的是趋化作用对行波速度的影响。我们证明了存在一个阈值，使得当相互作用比这更弱和更局部化时，趋化作用尽管不是平凡的，但不影响行波的速度；也就是说，最小速度的行波像FKPP情况一样具有速度2。另一方面，当相互作用是排斥的时，我们证明了在相互作用强度和长度尺度趋于无穷大的渐近区域内，最小行波速度是任意大的。
We examine a general model for the Fisher-KPP (FKPP) equation with nonlocal advection. The main interpretation of this model is as describing a diffusing and logistically growing population that is also influenced by intraspecific attraction or repulsion. For a particular choice of parameters, this specializes to the Keller-Segel-Fisher equation for chemotaxis. Our interest is in the effect of chemotaxis on the speed of traveling waves. We prove that there is a threshold such that, when interactions are weaker and more localized than this, chemotaxis, despite being non-trivial, does not influence the speed of traveling waves; that is, the minimal speed traveling wave has speed 2 as in the FKPP case. On the other hand, when the interaction is repulsive, we show that the minimal traveling wave speed is arbitrarily large in a certain asymptotic regime in which the interaction strength and length scale tend to infinity.