一类非对称非局部扩散时滞系统的单稳行波解  

Monostable Traveling Waves for a Class of Asymmetric System with Nonlocal Diffusion and Delay

作　　者：穆可旺 杨赟瑞 李孝武 MU KEWANG;YANG YUNRUI;LI XIAOWU(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,兰州730000

出　　处：《应用数学学报》2024年第6期869-891,共23页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(批准号:12361038)具有非局部效应的时滞非局部扩散系统的行波解和整体解;兰州交通大学百名青年优秀人才培养计划资助项目。

摘　　要：研究了一类非对称非局部扩散时滞系统(可以是非拟单调系统)的单稳行波解.首先,通过构造一对拟单调的上、下辅助系统将行波解的存在性转化为非线性算子的不动点问题,利用Schauder不动点定理和极限理论分别建立该系统非临界波速和临界波速下单稳行波解的存在性.其次,采用分析技术和Ikehara’s Tauberian定理研究了该系统单稳行波解的不存在性和渐近行为.最后,对所得的理论结果给出了具体的例子和数值模拟.The monostable traveling waves for a class of asymmetric system with nonlocal diffusion and delay(the system can be non-quasimonotone) are investigated. Firstly, the existence of traveling waves is transformed into the fixed point problem of a nonlinear operator by constructing a pair of super-auxiliary system and sub-auxiliary system with quasi-monotonicity, and thus the existence of monostable traveling waves under the non-critical and critical wave speed are established by using Schauder’s fixed point theorem and limiting argument, respectively. Secondly, the non-existence and asymptotic behaviors of monostable waves are discussed by analysis technique and Ikehara’s Tauberian theorem. Finally, concrete examples and numerical simulations for the obtained theoretical results are included.

关 键 词：非对称核 行波解 存在性 时滞 

分 类 号：O175.1[理学—数学]