Authors: Ai, Shangbing; Huang, Wenzhang

Source: Proceedings Section A: Mathematics - Royal Society of Edinburgh, Volume 135, Number 4, August 2005 , pp. 663-676(14)

Publisher: Royal Society of Edinburgh

Abstract:

The existence and uniqueness of travelling-wave solutions is investigated for a system of two reaction–diffusion equations where one diffusion constant vanishes. The system arises in population dynamics and epidemiology. Travelling-wave solutions satisfy a three-dimensional system about (u, u, ), whose equilibria lie on the u-axis. Our main result shows that, given any wave speed c > 0, the unstable manifold at any point (a, 0, 0) on the u-axis, where a (0, ) and is a positive number, provides a travelling-wave solution connecting another point (b, 0, 0) on the u-axis, where b := b(a) (, ), and furthermore, b(·) : (0, ) (, ) is continuous and bijective.

Document Type: Research article

Publication date: 2005-08-01

Related content

• In this: publication
• By this: publisher
• In this Subject: Mathematics and Statistics
• By this author: Ai, Shangbing ;  Huang, Wenzhang

Website © Publishing Technology. Article copyright remains with the publisher, society or author(s) as specified within the article.

• Terms and conditions
• Privacy policy
• Information for advertisers