Travelling front solutions of a nonlocal Fisher equation
Travelling front solutions of a nonlocal Fisher equation
复制标题
DOI：
10.1007/s002850000047
复制
发表时间：
2000-09
影响因子：
1.9
通讯作者：
S. A. Gourley
中科院分区：
文献类型：
--
作者：
S. A. Gourley
考虑一类含有非局部项（空间积分卷积）的标量反应扩散方程，Fisher方程是其中的一个特例。我们考虑连接方程的两个均匀状态的行波波前解。我们表明，如果非局部性是足够弱，在某种意义上，那么这样的旅行锋存在。我们还构造表达式的前和它的演变从初始数据，表明我们的前和Fisher方程之间的主要区别是，足够强的非局部性，我们的前是非单调的，有一个非常突出的驼峰。
We consider a scalar reaction-diffusion equation containing a nonlocal term (an integral convolution in space) of which Fisher‘s equation is a particular case. We consider travelling wavefront solutions connecting the two uniform states of the equation. We show that if the nonlocality is sufficiently weak in a certain sense then such travelling fronts exist. We also construct expressions for the front and its evolution from initial data, showing that the main difference between our front and that of Fisher‘s equation is that for sufficiently strong nonlocality our front is non-monotone and has a very prominent hump.