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Traveling Waves Solutions for Delayed Temporally Discrete Non-Local Reaction-Diffusion Equation

Author

Listed:
  • Hongpeng Guo

    (School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China)

  • Zhiming Guo

    (School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China)

Abstract

This paper deals with the existence of traveling wave solutions to a delayed temporally discrete non-local reaction diffusion equation model, which has been derived recently for a single species with age structure. When the birth function satisfies monotonic condition, we obtained the traveling wavefront by using upper and lower solution methods together with monotonic iteration techniques. Otherwise, without the monotonicity assumption for birth function, we constructed two auxiliary equations. By means of the traveling wavefronts of the auxiliary equations, using the Schauder’ fixed point theorem, we proved the existence of a traveling wave solution to the equation under consideration with speed c > c * , where c * > 0 is some constant. We found that the delayed temporally discrete non-local reaction diffusion equation possesses the dynamical consistency with its time continuous counterpart at least in the sense of the existence of traveling wave solutions.

Suggested Citation

  • Hongpeng Guo & Zhiming Guo, 2021. "Traveling Waves Solutions for Delayed Temporally Discrete Non-Local Reaction-Diffusion Equation," Mathematics, MDPI, vol. 9(16), pages 1-20, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1999-:d:618691
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    Cited by:

    1. Pasha, Syed Ahmed & Nawaz, Yasir & Arif, Muhammad Shoaib, 2023. "On the nonstandard finite difference method for reaction–diffusion models," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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