Exponential Stability of Traveling Waves for a Reaction Advection Diffusion Equation with Nonlinear-Nonlocal Functional Response

被引：0

作者：

Yan, Rui ^{[1
]}

Liu, Guirong ^{[2
]}

机构：

[1] Shanxi Univ Finance & Econ, Sch Appl Math, Taiyuan 030006, Shanxi, Peoples R China

[2] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China

来源：

DISCRETE DYNAMICS IN NATURE AND SOCIETY | 2017年 / 2017卷

基金：

中国国家自然科学基金;

关键词：

ASYMPTOTIC STABILITY; GLOBAL STABILITY; LOCAL STABILITY; FRONTS; EXISTENCE; MODEL;

D O I：

10.1155/2017/4614925

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The stability of a reaction advection diffusion equation with nonlinear-nonlocal functional response is concerned. By using the technical weighted energy method and the comparison principle, the exponential stability of all noncritical traveling waves of the equation can be obtained. Moreover, we get the rates of convergence. Our results improve the previous ones. At last, we apply the stability result to some real models, such as an epidemic model and a population dynamic model.

引用

页数：13

共 50 条

[21] Nonlinear stability of traveling wave fronts for nonlocal delayed reaction-diffusion equations [J].

Lv, Guangying ;

Wang, Mingxin .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 385 (02) :1094-1106

[22] Monostable traveling waves for a time-periodic and delayed nonlocal reaction-diffusion equation [J].

Li, Panxiao ;

Wu, Shi-Liang .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2018, 69 (02)

[23] Impact of nonlocal dispersal and time periodicity on the global exponential stability of bistable traveling waves [J].

Ma, Manjun ;

Meng, Wentao ;

Ou, Chunhua .

STUDIES IN APPLIED MATHEMATICS, 2023, 150 (03) :818-840

[24] Travelling waves and numerical approximations in a reaction advection diffusion equation with nonlocal delayed effects [J].

Liang, D ;

Wu, J .

JOURNAL OF NONLINEAR SCIENCE, 2003, 13 (03) :289-310

[25] Existence and stability of traveling wavefronts in a nonlocal diffusion equation with delay [J].

Pan, Shuxia ;

Li, Wan-Tong ;

Lin, Guo .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (06) :3150-3158

[26] Traveling waves in nonlocal delayed reaction-diffusion bistable equations and applications [J].

Li, Kun ;

He, Yanli .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2024, 47 (04) :2769-2786

[27] The asymptotic stability of diverging traveling waves for reaction-advection-diffusion equations in cylinders [J].

Jia, Fu-Jie ;

Wang, Zhi-Cheng ;

Guo, Gai-Hui .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2024, 75 (05)

[28] Existence and exponential stability of traveling waves for delayed reaction-diffusion systems [J].

Hsu, Cheng-Hsiung ;

Yang, Tzi-Sheng ;

Yu, Zhixian .

NONLINEARITY, 2018, 31 (03) :838-863

[29] Global stability of reaction-diffusion equation with nonlocal delay [J].

Qiu, Huanhuan ;

Ren, Beijia ;

Zou, Rong .

APPLIED MATHEMATICS LETTERS, 2025, 163

[30] Existence of Waves for a Nonlocal Reaction-Diffusion Equation [J].

Demin, I. ;

Volpert, V. .

MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2010, 5 (05) :80-101

← 1 2 3 4 5 →