CORE
🇺🇦
make metadata, not war
Services
Services overview
Explore all CORE services
Access to raw data
API
Dataset
FastSync
Content discovery
Recommender
Discovery
OAI identifiers
OAI Resolver
Managing content
Dashboard
Bespoke contracts
Consultancy services
Support us
Support us
Membership
Sponsorship
Community governance
Advisory Board
Board of supporters
Research network
About
About us
Our mission
Team
Blog
FAQs
Contact us
Slow travelling wave solutions of the nonlocal Fisher-KPP equation
Authors
John Billingham
Publication date
1 May 2020
Publisher
'IOP Publishing'
Doi
Cite
Abstract
© 2020 IOP Publishing Ltd & London Mathematical Society. We study travelling wave solutions, u = U(x - ct), of the nonlocal Fisher- KPP equation in one spatial dimension, dimension, (Display equation presented), with D = 1 and c = 1, where = = u is the spatial convolution of the population density, u(x, t), with a continuous, symmetric, strictly positive kernel, =(x), which is decreasing for x > 0 and has a finite derivative as x = 0+, normalized so that = = -= =(x)dx = 1. In addition, we restrict our attention to kernels for which the spatially-uniform steady state u = 1 is stable, so that travelling wave solutions have U = 1 as x - ct → - and U = 0 as x - ct→ for c > 0. We use the formal method of matched asymptotic expansions and numerical methods to solve the travelling wave equation for various kernels, =(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 =(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
Similar works
Full text
Open in the Core reader
Download PDF
Available Versions
Repository@Nottingham
See this paper in CORE
Go to the repository landing page
Download from data provider
oai:nottingham-repository.work...
Last time updated on 09/07/2019