# American Institute of Mathematical Sciences

February  2013, 33(2): 921-946. doi: 10.3934/dcds.2013.33.921

## Traveling fronts and entire solutions in partially degenerate reaction-diffusion systems with monostable nonlinearity

 1 Department of Mathematics, Xidian University, Xi’an, Shaanxi 710071 2 Department of Mathematics, Xidian University, Xi'an, Shaanxi 710071, China 3 Department of Applied Mathematics, Xidian University, Xi'an 710071

Received  August 2011 Revised  July 2012 Published  September 2012

This paper is concerned with traveling fronts and entire solutions for a class of monostable partially degenerate reaction-diffusion systems. It is known that the system admits traveling wave solutions. In this paper, we first prove the monotonicity and uniqueness of the traveling wave solutions, and the existence of spatially independent solutions. Combining traveling fronts with different speeds and a spatially independent solution, the existence and various qualitative features of entire solutions are then established by using comparison principle. As applications, we consider a reaction-diffusion model with a quiescent stage in population dynamics and a man-environment-man epidemic model in physiology.
Citation: Shi-Liang Wu, Yu-Juan Sun, San-Yang Liu. Traveling fronts and entire solutions in partially degenerate reaction-diffusion systems with monostable nonlinearity. Discrete & Continuous Dynamical Systems - A, 2013, 33 (2) : 921-946. doi: 10.3934/dcds.2013.33.921
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