Axially asymmetric traveling fronts in balanced bistable reaction-diffusion equations
Axially asymmetric traveling fronts in balanced bistable reaction-diffusion equations
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DOI：
10.1016/j.anihpc.2019.05.001
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发表时间：
2019-11
期刊：
影响因子：
--
通讯作者：
M. Taniguchi
中科院分区：
文献类型：
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作者：
M. Taniguchi
对于平衡的非线性反应扩散方程，一个轴对称的行波阵面是众所周知的。本文证明了平衡的非线性反应扩散方程存在轴对称的正速度波前。我们的方法如下。本文对一个非平衡反应扩散方程采用了一个金字塔形的波前，其横截面具有一个长轴和一个短轴。在保持长轴与短轴之比为常数的条件下，取平衡极限，得到了平衡扩散反应扩散方程的波前解。当常值比不为1时，该波前相对于运动轴单调递减，其横截面是一个具有长轴和短轴的紧集。
For a balanced bistable reaction-diffusion equation, an axisymmetric traveling front has been well known. This paper proves that an axially asymmetric traveling front with any positive speed does exist in a balanced bistable reaction-diffusion equation. Our method is as follows. We use a pyramidal traveling front for an unbalanced reaction-diffusion equation whose cross section has a major axis and a minor axis. Preserving the ratio of the major axis and a minor axis to be a constant and taking the balanced limit, we obtain a traveling front in a balanced bistable reaction-diffusion equation. This traveling front is monotone decreasing with respect to the traveling axis, and its cross section is a compact set with a major axis and a minor axis when the constant ratio is not 1.