University of Birmingham > Talks@bham > Applied Mathematics Seminar Series > Slow travelling wave solutions of the nonlocal Fisher-KPP equation

Slow travelling wave solutions of the nonlocal Fisher-KPP equation

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  • UserJohn Billingham, University of Nottingham
  • ClockThursday 05 December 2019, 13:00-14:00
  • HouseNuffield G13.

If you have a question about this talk, please contact Fabian Spill.

In this talk I will discuss travelling wave solutions, u = U(x-ct), of the nonlocal Fisher-KPP equation in one spatial dimension,

u_t = D u_xx + u(1-phiu)

with D << 1 and c << 1, where phiu is the spatial convolution of the population density, u(x,t), with a continuous, symmetric, strictly positive kernel, phi(x), which is decreasing for x>0 and has a finite derivative as x → 0+.

The formal method of matched asymptotic expansions and numerical methods can be used to solve the travelling wave equation for various kernels, phi(x), when c << 1. The most interesting feature of the leading order solution behind the wavefront is a sequence of tall, narrow spikes with O(1) weight, separated by regions where U is exponentially small. The regularity of phi(x) at x=0 is a key factor in determining the number and spacing of the spikes, and the spatial extent of the region where spikes exist.

This talk is part of the Applied Mathematics Seminar Series series.

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