非局部时滞反应扩散方程波前解的指数稳定性

李盼晓

doi:10.21656/1000-0887.380336

非局部时滞反应扩散方程波前解的指数稳定性

doi: 10.21656/1000-0887.380336

李盼晓

西安电子科技大学数学与统计学院, 西安 710071

基金项目: 国家自然科学基金(11671315)

详细信息

作者简介:
李盼晓(1990—),女,硕士(E-mail: L2236135404@163.com).

中图分类号: O175.14
计量
- 文章访问数: 982
- HTML全文浏览量: 108
- PDF下载量: 511
- 被引次数: 0
出版历程
- 收稿日期: 2017-12-28
- 修回日期: 2018-02-02
- 刊出日期: 2018-11-01

Exponential Stability of Traveling Wavefronts for ReactionDiffusion Equations With Delayed Nonlocal Responses

LI Panxiao

School of Mathematics and Statistics, Xidian University, Xi’an 710071, P.R.China

Funds: The National Natural Science Foundation of China(11671315)

摘要

摘要: 该文考虑了一类具有非局部时滞反应项的空间非局部扩散模型, 主要研究其波前解的渐近稳定性及收敛率.通过构造加权函数，建立了相关线性方程的比较原理，证明了当初始扰动在加权最大范数意义下一致有界，满足初值问题的解将依时间指数收敛到波前解，而且得到其指数收敛率.
- 行波解 /
- 非局部时滞 /
- 稳定性
Abstract: A spatially nonlocal diffusion model with a class of delayed nonlocal responses was considered. The asymptotic stability and the convergence rate of the traveling wavefronts were mainly studied. Through construction of weighted functions and establishment of a comparison principle for the related linear equations, the conclusion that if the initial function is within a bounded distance from a certain traveling wavefront with respect to a weighted maximum norm, the solution satisfying the initial value will converge to the traveling wavefront exponentially in time, was proved, and the exponential convergence rate was also obtained.
- traveling wave solution /
- nonlocal time delay /
- stability

HTML全文

参考文献(26)

[1]	FANG J, WEI J, ZHAO X Q. Spatial dynamics of a nonlocal and time-delayed reaction-diffusion system[J]. Journal of Differential Equations,2008,245(10): 2749-2770.
[2]	GOURLEY S A, WU J. Delayed non-local diffusive systems in biological invasion and disease spread[J]. Nonlinear Dynamics & Evolution Equations,2006,48: 137-200.
[3]	OU C, WU J. Persistence of wavefronts in delayed nonlocal reaction-diffusion equations[J]. Journal of Differential Equations,2007,235(1): 219-261
[4]	JOSEPH W H S, WU J, ZOU X. A reaction-diffusion model for a single species with age structure I: travelling wavefronts on unbounded domains[C]//Proceedings: Mathematical, Physical and Engineering Sciences,2012,457: 1841-1853.
[5]	THIEME H R, ZHAO X Q. Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models[J]. Journal of Differential Equations,2003,195(2): 430-470.
[6]	WANG Z C, LI W T, RUAN S. Traveling fronts in monostable equations with nonlocal delayed effects[J]. Journal of Dynamics & Differential Equations,2008,20(3): 573-607.
[7]	BRITTON N F. Spatial structures and periodic travelling waves in an integro-differential reaction-diffusion population model[J]. SIAM Journal on Applied Mathematics,1990,50(6): 1663-1688.
[8]	BRITTON N F. Aggregation and the competitive exclusion principle[J]. Journal of Theoretical Biology,1989,136(1): 57-66.
[9]	BATES P W, FIFE P C, REN X, et al. Traveling waves in a convolution model for phase transitions[J]. Archive for Rational Mechanics & Analysis,1997,138(2): 105-136.
[10]	BATES P W, CHMAJ A. A discrete convolution model for phase transitions[J]. Archive for Rational Mechanics & Analysis,1999,150(4): 281-368.
[11]	COVILLE J. On uniqueness and monotonicity of solutions of non-local reaction diffusion equation[J]. Annali di Matematica Pura ed Applicata,2006,185(3): 461-485.
[12]	COVILLE J, DUPAIGNE L. Propagation speed of travelling fronts in non local reaction-diffusion equations[J]. Nonlinear Analysis: Theory, Methods & Applications,2005,60(5): 797-819.
[13]	COVILLE J, DUPAIGNE L. On a non-local eqution arising in population dynamics[J]. Proceedings of the Royal Society of Edinburgh Section A: Mathematics,2007,137(4): 727-755.
[14]	YU Z, YUAN R. Existence, asymptotic and uniqueness of traveling waves for nonlocal diffusion systems with delayed nonlocal response[J]. Taiwanese Journal of Mathematics,2013,17(6): 2163-2190.
[15]	GUO S, ZIMMER J. Travelling wavefronts in nonlocal diffusion equations with nonlocal delay effects[J]. Bulletin of the Malaysian Mathematical Sciences Society,2018,41(2): 919-943.
[16]	CHENG H, YUAN R. Stability of traveling wave fronts for nonlocal diffusion equation with delayed nonlocal response[J]. Taiwanese Journal of Mathematics,2016,20(4): 801-822.
[17]	GUO S, ZIMMER J. Stability of travelling wavefronts in discrete reaction-diffusion equations with nonlocal delay effects[J]. Nonlinearity,2015,28(2): 463-492.
[18]	MEI M, OU C, ZHAO X Q. Global stability of monostable traveling waves for nonlocal time-delayed reaction-diffusion equations[J]. SIAM Journal on Mathematical Analysis,2010,42(6): 2762-2790.
[19]	MA S, ZHAO X Q. Global asymptotic stability of minimal fronts in monostable lattice equations[J]. Discrete and Continuous Dynamical Systems,2008,21(1): 259-275.
[20]	OUYANG Z, OU C. Global stability and convergence rate of traveling waves for a nonlocal model in periodic media[J]. Discrete and Continuous Dynamical Systems (Series B),2012,17(3): 993-1007.
[21]	邢伟, 颜七笙, 杨志辉, 等. 一类具有非线性传染率的SEIS传染病模型的稳定性分析[J]. 应用数学和力学, 2016, 37(11): 1247-1254.(XING Wei, YAN Qisheng, YANG Zhihui. Stability analysis of an SEIS epidemic model with a nonlinear incidence rate[J]. Applied Mathematics and Mechanics,2016,37(11): 1247-1254.(in Chinese))
[22]	谢英超, 程燕, 贺天宇. 一类具有非线性发生率的时滞传染病模型的全局稳定性[J]. 应用数学和力学, 2015,36(10): 1107-1116.(XIE Yingchao, CHENG Yan, HE Tianyu. Global stability of a class of delayed epidemic models with nonlinear incidence rates[J]. Applied Mathematics and Mechanics,2015,36(10): 1107-1116.(in Chinese))
[23]	WU S L, CHEN G. Uniqueness and exponential stability of traveling wave fronts for a multi-type SIS nonlocal epidemic model[J]. Nonlinear Analysis: Real World Applications,2017,36: 267-277.
[24]	CHEN X, GUO J S. Existence and asymptotic stability of traveling waves of discrete quasilinear monostable equations[J]. Journal of Differential Equations,2002,184(2): 549-569.
[25]	WANG X S, ZHAO X Q. Pulsating waves of a partially degenerate reaction-diffusion system in a periodic habitat[J]. Journal of Differential Equations,2015,259(12): 7238-7259.
[26]	WU Y, XING X. Stability of traveling waves with critical speeds for p-degree Fisher-type equations[J]. Discrete and Continuous Dynamical Systems,2008,20(4): 1123-1139.