非局部扩散Holling-Tanner捕食者-食饵系统的临界与非临界行波解分析  

Analysis on Critical Waves and Non-Critical Waves for Holling-Tanner Predator-Prey System with Nonlocal Diffusion

作　　者：吴鑫 袁荣[2] 马兆海 Wu Xin;Yuan Rong;Ma Zhaohai(School of Sciences,East China Jiaotong University,Nanchang 330013;School of Mathematical Sciences,Beijing Normal University,Beijing 100875;School of Science,China University of Geosciences,Beijing 100083)

机构地区：[1]华东交通大学理学院,南昌330013 [2]北京师范大学数学科学学院,北京100875 [3]中国地质大学(北京)数理学院,北京100083

出　　处：《数学物理学报（A辑）》2021年第6期1705-1717,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(11771044,11871007,12001502);江西省自然科学基金(20202BABL211003);江西省教育厅科技项目(GJJ180354);中央高校基本科研基金(2652019015)。

摘　　要：该文改进了文献[2]关于Holling-Tanner捕食者-食饵系统行波解的最新结果.结果表明:存在常数c^(*)>0使得对任意的c>c^(*),在假设条件■(ξ)<1和■(ξ)>0下,该系统有一个波速为c的连接常数稳态解(1,0)和(1/1+β,1/1+β)的行波解(u(ξ),v(ξ)).该文去掉这些技术假设,并通过一些分析技术得到c>c^(*)时行波解的存在性.进而利用逼近方法得到临界行波解的存在性,从而解决了文献[2]中的公开性问题.值得指出的是模型中系统的耦合性与非局部扩散都给行波解的研究带来了困难.In the current paper we improve the recent results established in[2]concerning the traveling wave solutions for a Holling-Tanner predator-prey system.It is shown that there is a c^(*)>0 such that for every c>c^(*),this system has a traveling wave solution(u(ξ),v(ξ)with speed c connecting the constant steady states(1,0)and(1/1+β,1/1+β)under the technical assumptions■(ξ)<1 and■(ξ)>0.Here we do not assume these assumptions and obtain the existence of traveling waves for every c>c^(*)by some analysis techniques.Moreover,we deal with the open problem in[2]and complete the study of traveling waves with the critical wave speed c^(*)by the approximating method.We also point out that both the nonlocal dispersal and coupling of the system in the model bring some difficulties in the study of traveling wave solutions.

关 键 词：临界行波解 非临界行波解 捕食者-食饵系统 非局部扩散 反应扩散方程 

分 类 号：O175[理学—数学]