@article {Ai:2005-08-01T00:00:00:0308-2105:663,
author = "Ai, Shangbing and 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",
number = "4",
year = "2005-08-01T00:00:00",
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*(*ยท*) : (0, **) → (*, ∞*) is continuous and bijective.",
pages = "663-676",
url = "http://www.ingentaconnect.com/content/rse/proca/2005/00000135/00000004/art00001"
}