非局部扩散的时空时滞霍乱传染病系统的行波解

数学物理学报 ›› 2025, Vol. 45 ›› Issue (1): 110-135.

非局部扩散的时空时滞霍乱传染病系统的行波解

杨咏丽, 杨赟瑞^*

兰州交通大学数理学院兰州 730070

收稿日期:2024-01-29 修回日期:2024-05-15 出版日期:2025-02-26 发布日期:2025-01-08
通讯作者: *杨赟瑞,E-mail: yl051199@163.com
作者简介:杨咏丽, E-mail: lily1979101@163.com
基金资助:
国家自然科学基金 (12361038) 和兰州交通大学百名青年优秀人才培养计划

Traveling Wave Solutions to a Cholera Epidemic System with Spatio-Temporal Delay and Nonlocal Dispersal

Yang Yongli, Yang Yunrui

School of Mathematics, Physics, Lanzhou Jiaotong University, Lanzhou 730070

Received:2024-01-29 Revised:2024-05-15 Online:2025-02-26 Published:2025-01-08
Supported by:
National Natural Science Foundation of China (12361038) and the Foundation of a Hundred Youth Talents Training Program of Lanzhou Jiaotong University

摘要/Abstract

摘要： 该文研究了一类非局部扩散的时空时滞霍乱传染病系统行波解的存在性、不存在性和渐近行为. 通过构造上下解, 将行波解的存在性问题转化为闭凸锥上非线性算子存在不动点的问题, 再借助Schauder不动点定理、极限理论和分析技术证明该系统行波解的存在性、有界性和负无穷远处的渐近行为. 此外, 基于双边 Laplace 变换和反证法建立该系统行波解的不存在性.

关键词: 非局部扩散, 时空时滞, 行波解

Abstract: This paper deals with the existence, non-existence and asymptotic behaviors of traveling wave solutions to a class of cholera epidemic system with spatio-temporal delay and nonlocal dispersal. By constructing the upper and lower solutions, the existence of traveling waves to the system is converted into the fixed point problem of a nonlinear operator on a closed and convex cone, and thus the existence, boundedness and asymptotic behavior at negative infinity of traveling waves of the system are proved by applying Schauder's fixed point theorem, limit theory and analysis techniques. In addition, the nonexistence of traveling waves of the system is also established based on the two-sided Laplace transform and the method of proof by contradiction.

Key words: nonlocal dispersal, spatio-temporal delay, traveling wave solutions

中图分类号:

O175

杨咏丽, 杨赟瑞. 非局部扩散的时空时滞霍乱传染病系统的行波解[J]. 数学物理学报, 2025, 45(1): 110-135.

Yang Yongli, Yang Yunrui. Traveling Wave Solutions to a Cholera Epidemic System with Spatio-Temporal Delay and Nonlocal Dispersal[J]. Acta mathematica scientia,Series A, 2025, 45(1): 110-135.

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