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

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.