Planar Standing Wavefronts in the FitzHugh-Nagumo Equations
Planar Standing Wavefronts in the FitzHugh-Nagumo Equations
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DOI：
10.1137/130907793
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发表时间：
2014-02
期刊：
影响因子：
--
通讯作者：
Chao-Nien Chen;S. Kung;Y. Morita
中科院分区：
文献类型：
--
作者：
Chao-Nien Chen;S. Kung;Y. Morita
本文研究了Fitzhugh-Nagumo方程的驻波问题。Fitzhugh-Nagumo方程是一种著名的具有图灵花样的激活剂-抑制剂型反应扩散模型。与Allen-Cahn方程类似，在研究平面驻波前的存在时，对由反应项引起的势施加了一个平衡条件。此外，激活剂和缓蚀剂的扩散速率必须在适当的范围内，才能确保这种波的存在。对于具有对称性的立面，应用比较论元产生唯一性结果。此外，还分析了相移前波前的渐近稳定性。
This article is devoted to the investigation of standing waves for the FitzHugh--Nagumo equations, a well-known reaction-diffusion model of activator-inhibitor type for exhibiting Turing patterns. Similar to the Allen--Cahn equation, a balanced condition for the potential induced from the reaction terms is imposed in studying the existence of planar standing wavefronts. Furthermore, the diffusion rates of activator and inhibitor must be in an appropriate range to ensure the existence of such waves. For the standing front with a symmetry property, an application of the comparison argument yields a uniqueness result. Moreover, the asymptotic stability of wavefronts up to a phase shift is analyzed.