SPATIAL DYNAMICS OF THE ADVECTIVE REACTION-DIFFUSION EQUATION ON FUNNEL-SHAPED DOMAINS

Yan Zhang; Bang-Sheng Han; Hong-Lei Wei; Yinghui Yang

doi:10.11948/20240267

2025 Volume 15 Issue 5

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Yan Zhang, Bang-Sheng Han, Hong-Lei Wei, Yinghui Yang. SPATIAL DYNAMICS OF THE ADVECTIVE REACTION-DIFFUSION EQUATION ON FUNNEL-SHAPED DOMAINS[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2551-2569. doi: 10.11948/20240267

Citation:

Yan Zhang, Bang-Sheng Han, Hong-Lei Wei, Yinghui Yang. SPATIAL DYNAMICS OF THE ADVECTIVE REACTION-DIFFUSION EQUATION ON FUNNEL-SHAPED DOMAINS[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2551-2569. doi: 10.11948/20240267

SPATIAL DYNAMICS OF THE ADVECTIVE REACTION-DIFFUSION EQUATION ON FUNNEL-SHAPED DOMAINS

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

Author Bio: Email: zhangyan1999@my.swjtu.edu.cn(Y. Zhang); Email: weihonglei1981@163.com(H.-L. Wei); Email: yangyh8605@swjtu.edu.cn(Y. Yang)
Corresponding author: Email: hanbangsheng@swjtu.edu.cn(B.-S. Han)

Abstract

Abstract

This paper is concerned with the entire solution of the advective reaction-diffusion equation with the bistable nonlinear reaction term on funnel-shaped domains. We focus on the well-posedness and long-time behavior of the entire solution. Because of the impact of advection, the previous super and sub-solutions are no longer applicable, so we study the existence of the entire solution behaving as a planar front by constructing appropriate super-solutions and sub-solutions. In addition, we show the uniqueness and Lyapunov stability of the entire solution. This is probably the first study of the advective reaction-diffusion on funnel-shaped domains.
- Reaction-diffusion equation /
- advective /
- bistable /
- entire solution
MSC: 35B08, 35C07, 35K40, 35K57

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References

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