状态依赖时滞的非局部扩散方程的行波解存在性

在自然界中,非局部扩散现象更广泛存在,因此,对非局部扩散方程的研究更具现实意义。在研究扩散系统的过程中,为了克服非局部扩散问题,常用卷积算子或积分微分方程研究扩散系统。基于状态依赖时滞的非局部的种群模型行波解存在性的研究,研究了更一般的状态依赖时滞的非局部扩散方程的行波解存在性。通过利用合适的上下解及有关假设构造一个算子所在的集合;通过Schauder不动点定理,证明了当波速大于临界波速时单调行波解(波前解)的存在性。

Existence of traveling waves solutions of the nonlocal dispersal equation with state-dependent delay

In nature, the phenomenon of non-local diffusion is widespread, therefore, the study of the nonlocal dispersal equation is of practical significance. Usually, the dispersal system is studied by using the convolution operator or the integral differential equation. Based on the study of the traveling waves solutions of the nonlocal equation with state-dependent delay, the traveling waves solutions of the more general nonlocal dispersal equation with state-dependent delay were concerned. By applying the appropriate upper and lower solutions and relevant assumptions, the set of an operator was constructed. By using Schauder fixed point theorem, the existence of traveling waves is proved when the wave velocity is greater than the critical wave velocity.