带有非局部扩散项的霍乱传染病模型行波解的存在性  

Traveling Waves in a Nonlocal Dispersal Cholera Model

作　　者：杨炜明[1] 廖书[2] 方芳[3] YANG Weiming;LIAO Shu;FANG Fang(Chongqing Key Laboratory of Social Economic and Applied Statistics,School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China;School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China;College of Foreign Languages,Chongqing Technology and Business University,Chongqing 400067,China)

机构地区：[1]重庆工商大学社会经济应用统计重庆市重点实验室,数学与统计学院,重庆400067 [2]重庆工商大学数学与统计学院,重庆400067 [3]重庆工商大学外语学院,重庆400067

出　　处：《应用数学学报》2021年第3期440-458,共19页Acta Mathematicae Applicatae Sinica

基　　金：重庆市基础研究与前沿探索项目(No.cstc2020jcyj-msxmX0394);重庆市教委科学技术研究项目(No.KJQN201900806);经济社会应用统计重庆市重点实验室开放课题(KFJJ2018067)资助.

摘　　要：本文主要研究带有非局部扩散项的霍乱传染病模型行波解的存在性问题.首先当R0>1,c>c^(*)时,利用Schauder不动点定理,构造了一对上下解,从而得到行波解的存在性.其次巧妙的构造Lyapunov函数结合Lebesgue控制收敛定理,得到行波解在+∞处的渐近行为.最后再研究当R0>1,c=c^(*)时模型行波解的存在性.In this paper,we study a nonlocal dispersal cholera model.The existence of traveling wave solutions is obtained by applying Schauder’s fixed point theorem with upperlower solutions in the case of R0>1 with c>c^(*).Moreover,we construct suitable Lyapunov function to analyze the boundary asymptotic behavior of traveling wave solutions at+∞.Finally,we show the existence of the traveling wave solutions in the case of R0>1 with c=c^(*).

关 键 词：SCHAUDER不动点定理 传染病模型 非局部扩散 LEBESGUE控制收敛定理 行波解 Lyapunov函数 渐近行为 上下解 

分 类 号：O212.7[理学—概率论与数理统计]