Traveling waves and their stability in a coupled reaction diffusion system

Xiaojie Hou; Wei Feng

doi:10.3934/cpaa.2011.10.141

Article Contents

2011, Volume 10, Issue 1: 141-160. Doi: 10.3934/cpaa.2011.10.141

This issue Previous Article Improved almost Morawetz estimates for the cubic nonlinear Schrödinger equation Next Article Blowing up at zero points of potential for an initial boundary value problem

Traveling waves and their stability in a coupled reaction diffusion system

Xiaojie Hou^1, and
Wei Feng^2,

1.
Department of Mathematics and Statistics, University of North Carolina at Wilmington, Wilmington, NC 28403
2.
Department of Mathematics and Statistics, UNC Wilmington, Wilmington, NC 28403

Received: December 31, 2009

Revised: April 30, 2010

Published: December 2010

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Abstract

We study the traveling wave solutions to a reaction diffusion system modeling the public goods game with altruistic behaviors. The existence of the waves is derived through monotone iteration of a pair of classical upper- and lower solutions. The waves are shown to be unique and strictly monotonic. A similar KPP wave like asymptotic behaviors are obtained by comparison principle and exponential dichotomy. The stability of the traveling waves with non-critical speed is investigated by spectral analysis in the weighted Banach spaces.

Keywords:

Mathematics Subject Classification: Primary: 35B35; Secondary: 91B18, 35K57, 35B40, 35P15.

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