Monotonicity, uniqueness, and stability of traveling waves in a nonlocal reaction-diffusion system with delay

被引：1

作者：

Zhao, Hai-Qin ^{[1
]}

机构：

[1] Xidian Univ, Sch Math & Stat, Xian 710071, Shaanxi, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2017年 / 40卷 / 18期

关键词：

epidemic model; monostable nonlinearity; reaction-diffusion system; traveling waves; ASYMPTOTIC STABILITY; EPIDEMIC MODEL; MONOSTABLE EQUATIONS; GLOBAL STABILITY; FRONTS; SPREAD; EXISTENCE; SPEEDS; NONLINEARITY;

D O I：

10.1002/mma.4483

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to study the traveling wave solutions of a nonlocal reaction-diffusion system with delay arising from the spread of an epidemic by oral-faecal transmission. Under monostable and quasimonotone it is well known that the system has a minimal wave speed c* of traveling wave fronts. In this paper, we first prove the monotonicity and uniqueness of traveling waves with speed c >= c*. Then we show that the traveling wave fronts with speed c > c* are exponentially asymptotically stable.

引用

页码：6702 / 6714

页数：13

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