Differential and Integral Equations

A reaction-diffusion system on noncoincident spatial domains modeling the circulation of a disease between two host populations

W. E. Fitzgibbon, M. Langlais, and J. J. Morgan

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Abstract

We study the global existence and long-time behavior of the solutions to a special reaction-diffusion system arising in mathematical population dynamics, with kinetics occurring on distinct spatial domains. First, we give a comprehensive description of the dynamics of the solutions of the underlying system of ordinary differential equations. Next, we analyze a simpler problem where the spatial domain is the same for all the partial differential equations. Last, we prove global existence for the original problem; we offer a conjecture concerning the large-time behavior of solutions and give some hints on its derivation and proof.

Article information

Source
Differential Integral Equations Volume 17, Number 7-8 (2004), 781-802.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060329

Mathematical Reviews number (MathSciNet)
MR2074686

Zentralblatt MATH identifier
1150.35448

Subjects
Primary: 35K57: Reaction-diffusion equations
Secondary: 35K50 92D30: Epidemiology

Citation

Fitzgibbon, W. E.; Langlais, M.; Morgan, J. J. A reaction-diffusion system on noncoincident spatial domains modeling the circulation of a disease between two host populations. Differential Integral Equations 17 (2004), no. 7-8, 781--802. https://projecteuclid.org/euclid.die/1356060329.


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