@article {Ai:August 2005:0308-2105:663,
author = "Ai, Shangbing",
author = "Huang, Wenzhang",
title = "Travelling waves for a reaction-diffusion system in population dynamics and epidemiology",
journal = "Proceedings Section A: Mathematics - Royal Society of Edinburgh",
volume = "135",
year = "August 2005",
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.",
pages = "663-676(14)",
url = "http://www.ingentaconnect.com/content/rse/proca/2005/00000135/00000004/art00001"
}