The Approach of Solutions for the Nonlocal Diffusion Equation to Traveling Fronts

The Approach of Solutions for the Nonlocal Diffusion Equation to Traveling Fronts

Year:    2020

Author:    Shaohua Gan, Zhixian Yu

Journal of Nonlinear Modeling and Analysis, Vol. 2 (2020), Iss. 2 : pp. 205–226

Abstract

The paper is concerned with the asymptotic behavior as $t → ±∞$ of an entire solution $u(x, t)$ for the nonlocal diffusion equation. With bistable assumption, it is well known that the model has three different types of traveling fronts. Under certain conditions on the wave speeds, and by some auxiliary rational functions with certain properties to construct appropriate super- and sub- solutions of the model, we establish two new types of entire solutions $u(x, t)$ which approach to three travelling fronts or the positive equilibrium as $t → ±∞$.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.12150/jnma.2020.205

Journal of Nonlinear Modeling and Analysis, Vol. 2 (2020), Iss. 2 : pp. 205–226

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Entire solution Traveling front Nonlocal evolution equation Super-sub solutions.

Author Details

Shaohua Gan

Zhixian Yu