Communications on Pure and Applied Analysis (CPAA)

Traveling waves and their stability in a coupled reaction diffusion system

Pages: 141 - 160, Volume 10, Issue 1, January 2011      doi:10.3934/cpaa.2011.10.141

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Xiaojie Hou - Department of Mathematics and Statistics, University of North Carolina at Wilmington, Wilmington, NC 28403, United States (email)
Wei Feng - Department of Mathematics and Statistics, UNC Wilmington, Wilmington, NC 28403, United States (email)

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:  Traveling wave, existence, asymptotic rates, uniqueness, spectrum, stability.
Mathematics Subject Classification:  Primary: 35B35; Secondary: 91B18, 35K57, 35B40, 35P15.

Received: January 2010;      Revised: May 2010;      Available Online: November 2010.