非局部时滞扩散方程棱锥形波前解的渐近稳定性  

Asymptotic Stability of Pyramidal Traveling Front for Nonlocal Delayed Diffusion Equation

作　　者：刘佳 包雄雄 Jia Liu;Xiongxiong Bao(School of Sciences,Chang'an University,Xi'an 710064)

机构地区：[1]长安大学理学院,西安710064

出　　处：《数学物理学报(A辑)》2025年第1期44-53,共10页Acta Mathematica Scientia

基　　金：国家自然科学基金(12271058);陕西省自然科学基金(2023-JC-YB-023,2021JQ-218)。

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R^(N)(N≥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.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 R^(N) with N≥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 R^(3) is uniquely determined,which is asymptotically stable when the initial perturbations decay at infinity.

关 键 词：棱锥形行波解 反应扩散方程 非局部时滞 稳定性 

分 类 号：O175.2[理学—数学]