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
Math. Comput. Appl. 2010, 15(5), 762-767; https://doi.org/10.3390/mca15050762
Submission received: 31 December 2010
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Accepted: 31 December 2010
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Published: 31 December 2010
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.
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MDPI and ACS Style
Ge, Z. Dynamical Behaviors of a Delayed Reaction-Diffusion Equation. Math. Comput. Appl. 2010, 15, 762-767. https://doi.org/10.3390/mca15050762
AMA Style
Ge Z. Dynamical Behaviors of a Delayed Reaction-Diffusion Equation. Mathematical and Computational Applications. 2010; 15(5):762-767. https://doi.org/10.3390/mca15050762
Chicago/Turabian StyleGe, Zhihao. 2010. "Dynamical Behaviors of a Delayed Reaction-Diffusion Equation" Mathematical and Computational Applications 15, no. 5: 762-767. https://doi.org/10.3390/mca15050762
