Travelling wave phenomena in non-linear diffusion degenerate Nagumo equations
Travelling wave phenomena in non-linear diffusion degenerate Nagumo equations
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DOI：
10.1007/s002850050073
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发表时间：
1997-06
影响因子：
1.9
通讯作者：
F. Sánchez-Garduño;P. Maini
中科院分区：
文献类型：
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作者：
F. Sánchez-Garduño;P. Maini
本文研究了非线性退化（atu=0）反应扩散方程[D(u)ux]x+g(u)的一维行波解su(x, t)=φ(x−ct)的存在性，这是神经传导理论中出现的Nagumo方程的推广，并描述了allee效应。我们使用动力系统方法来证明：1。一个异斜循环（两个单调平稳前解）的全局分岔，力= 0,2。证明了φ(x−c*t)是sharp型和3的行波解的唯一值c*>的存在性。单调和振荡锋面力≠c*的连续统。本文给出了行波坐标系下和全偏微分方程下的相像的数值模拟。
In this paper we study the existence of one-dimensional travelling wave solutionsu(x, t)=φ(x−ct)for the non-linear degenerate (atu=0) reaction-diffusion equationut=[D(u)ux]x+g(u)wheregis a generalisation of the Nagumo equation arising in nerve conduction theory, as well as describing theAllee effect. We use a dynamical systems approach to prove: 1. the global bifurcation of a heteroclinic cycle (two monotone stationary front solutions), forc=0, 2. The existence of a unique valuec*>0 ofcfor which φ(x−c*t)is a travelling wave solution of sharp type and 3. A continuum of monotone and oscillatory fronts forc≠c*. We present some numerical simulations of the phase portrait in travelling wave coordinates and on the full partial differential equation.