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Math. Comput. Appl. 2010, 15(5), 762-767; doi:10.3390/mca15050762

Dynamical Behaviors of a Delayed Reaction-Diffusion Equation

Institute of Applied Mathematics School of Mathematics and Information Sciences Henan University, 475004 Kaifeng, Henan, P.R. China
Received: 31 December 2010 / Accepted: 31 December 2010 / Published: 31 December 2010
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Abstract

In this paper, we derive a delayed reaction-diffusion equation to describe a two-species predator-prey system with diffusion terms and stage structure. By coupling the uniformly approximate approach with the method of upper and lower solutions, we prove that the traveling wave fronts exist, which connect the zero solution with the positive steady state. Finally, we draw a conclusion that the existence of traveling wave fronts for the delayed reaction-diffusion equation is an interesting and difficult problem.
Keywords: Reaction-Diffusion Equations; Asymptotical Stability; Traveling Wave fronts Reaction-Diffusion Equations; Asymptotical Stability; Traveling Wave fronts
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Ge, Z. Dynamical Behaviors of a Delayed Reaction-Diffusion Equation. Math. Comput. Appl. 2010, 15, 762-767.

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