非局部时滞扩散方程棱锥形波前解的渐近稳定性

数学物理学报 ›› 2025, Vol. 45 ›› Issue (1): 44-53.

非局部时滞扩散方程棱锥形波前解的渐近稳定性

刘佳(),包雄雄^*()

长安大学理学院西安 710064

收稿日期:2023-10-28 修回日期:2024-05-25 出版日期:2025-02-26 发布日期:2025-01-08
通讯作者: * 包雄雄, E-mail:baoxx2016@chd.edu.cn
作者简介:刘佳,E-mail:liujia@chd.edu.cn
基金资助:
国家自然科学基金(12271058);陕西省自然科学基金(2023-JC-YB-023);陕西省自然科学基金(2021JQ-218)

Asymptotic Stability of Pyramidal Traveling Front for Nonlocal Delayed Diffusion Equation

Liu Jia(),Bao Xiongxiong^*()

School of Sciences, Chang'an University, Xi'an 710064

Received:2023-10-28 Revised:2024-05-25 Online:2025-02-26 Published:2025-01-08
Supported by:
NSFC(12271058);Natural Science Basic Research Plan in Shanxi Province of China(2023-JC-YB-023);Natural Science Basic Research Plan in Shanxi Province of China(2021JQ-218)

摘要/Abstract

摘要：

反应扩散方程的非平面行波解吸引了许多专家学者的关注. 在高维空间 $\Bbb{R}^{N}$ ($N\geq 3$) 中, 非局部时滞扩散方程的棱锥形行波解的存在性已经被证明. 事实上, 这样的 $N$ 维棱锥形行波解的唯一性与稳定性是非常有意义的研究问题. 该文证明了在 $\Bbb{R}^{3}$ 中, 非局部时滞扩散方程的棱锥形行波解是唯一确定的, 并且当初始扰动在无穷远处衰减时棱锥形行波解也是渐近稳定的.

关键词: 棱锥形行波解, 反应扩散方程, 非局部时滞, 稳定性.

Abstract:

The nonplanar traveling fronts of reaction-diffusion equations have been attracted a lot of attention and pyramidal traveling fronts for the nonlocal delayed diffusion equation are also established in $\Bbb{R}^{N}$ with $N\geq 3$. In fact, the uniqueness and stability for such $N$-dimensional pyramidal traveling fronts are very interesting problems. The current paper shows that the pyramidal traveling front for the nonlocal delayed diffusion equation in $\Bbb{R}^{3}$ is uniquely determined, which is asymptotically stable when the initial perturbations decay at infinity.

Key words: pyramidal traveling wave solution, reaction-diffusion equation, nonlocal delayed, stability.

中图分类号:

O175.2

刘佳, 包雄雄. 非局部时滞扩散方程棱锥形波前解的渐近稳定性[J]. 数学物理学报, 2025, 45(1): 44-53.

Liu Jia, Bao Xiongxiong. Asymptotic Stability of Pyramidal Traveling Front for Nonlocal Delayed Diffusion Equation[J]. Acta mathematica scientia,Series A, 2025, 45(1): 44-53.

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