PROPAGATING TERRACE IN A PERIODIC REACTION-DIFFUSION EQUATION WITH CONVECTION

Liang-Bin Shen; Bang-Sheng Han

doi:10.11948/20230239

2024 Volume 14 Issue 3

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Liang-Bin Shen, Bang-Sheng Han. PROPAGATING TERRACE IN A PERIODIC REACTION-DIFFUSION EQUATION WITH CONVECTION[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1395-1413. doi: 10.11948/20230239

Citation:

Liang-Bin Shen, Bang-Sheng Han. PROPAGATING TERRACE IN A PERIODIC REACTION-DIFFUSION EQUATION WITH CONVECTION[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1395-1413. doi: 10.11948/20230239

PROPAGATING TERRACE IN A PERIODIC REACTION-DIFFUSION EQUATION WITH CONVECTION

Liang-Bin Shen^1,,
Bang-Sheng Han^1, ,

1.
School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 611756, China

Author Bio: Email: shenliangbin2020@163.com(L.-B. Shen)
Corresponding author: Email: hanbangsheng@swjtu.edu.cn(B.-S. Han)

Abstract

Abstract

In this paper, we study the asymptotic properties of the solution for a space periodic reaction-diffusion equation with convection term. Firstly, we introduce the zero-number parameter method to compare the steepness of different solutions, so as to obtain the convergence of solution and the existence of the minimal propagating terrace. To be exact, the minimal propagating terrace is composed of individual pulsating traveling waves. By constructing the $ \omega $-limit set, we prove that the existence of pulsating traveling waves. Secondly, the stability theory is a necessary condition for the existence of the propagating terrace. Contrary to conventional conclusions, there we first consider extend the stability theory of the classical reaction-diffusion equation to the reaction-diffusion equation with convection term, and through constructing the Cauchy problem of the initial boundary value to solve the stability problem of the equation solution. Besides, we are especially concerned with the minimal propagating terrace existence, uniqueness, and their spatial structure.
- Spatial period /
- convective term /
- pulsating wave /
- minimal propagating terrace /
- limit set
MSC: 35B35, 35K15, 35K57, 92D25

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References

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