Traveling waves and their stability in a coupled reaction diffusion system
Xiaojie Hou - Department of Mathematics and Statistics, University of North Carolina at 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,
Received: January 2010; Revised: May 2010; Published: November 2010.
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