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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Previous articles were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence, and they are hosted by MDPI on mdpi.com as a courtesy and upon agreement with Association for Scientific Research (ASR).
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Article

Dynamical Behaviors of a Delayed Reaction-Diffusion Equation

by
Zhihao Ge
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 / Accepted: 31 December 2010 / Published: 31 December 2010
Versions Notes

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

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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 Style

Ge, 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

APA Style

Ge, Z. (2010). Dynamical Behaviors of a Delayed Reaction-Diffusion Equation. Mathematical and Computational Applications, 15(5), 762-767. https://doi.org/10.3390/mca15050762

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