带非局部扩散项的一般性霍乱模型的行波解  

Traveling Wave Solution of a General Cholera Model with Non-local Diffusion

作　　者：廖书[1,2] 方章英 LIAO Shu;FANG Zhangying(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China;Chongqing Key Laboratory of Social Economy and Applied Statistics,Chongqing Technology and Business University,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]重庆工商大学经济社会应用统计重庆市重点实验室,重庆400067

出　　处：《应用数学》2023年第2期327-342,共16页Mathematica Applicata

基　　金：重庆市基础研究与前沿探索项目(cstc2020jcyj-msxmX0394);重庆市教委科学技术研究项目(KJQN201900806)。

摘　　要：本文研究一类具有一般性的带非局部扩散项的霍乱模型,用不同的函数表示人与人之间以及人与环境之间的发生率,以及霍乱病菌的增长函数.当R0>1,c>c∗时,通过构造上下解函数,结合Schauder不动点定理讨论该模型行波解的存在性,再构造Lyapunov函数讨论行波解的渐近性.当c<c∗时,通过双边拉普拉斯变换和Fatou引理证明该模型行波解的不存在性.This paper investigates a class of cholera models with non-local diffusion terms with general characteristics,using different functions to represent the incidence between people and between people and the environment,as well as the growth function of cholera pathogens.When R0>1,c>c∗,by constructing the upper and lower solution functions,combined with the Schauder fixed-point theorem to discuss the existence of the model’s traveling-wave solution,and then constructing the Lyapunov function to discuss the asymptoticity of the traveling-wave solution,when c<c∗,the non-existence of the model’s row-wave solution was proved by bilateral Laplace transforms and Fatou lemmas.

关 键 词：一般性霍乱模型 非局部扩散项 行波解 Shauder不动点定理 LYAPUNOV函数 

分 类 号：O29[理学—应用数学]