带有时空时滞的混合扩散竞争系统的行波解

石玲玲; 王飏; 姚美萍

doi:10.13451/j.sxu.ns.2024010

山西大学学报(自然科学版) ›› 2025, Vol. 48 ›› Issue (03) : 429 -434. DOI: 10.13451/j.sxu.ns.2024010

基础数学与应用数学

带有时空时滞的混合扩散竞争系统的行波解

石玲玲 ¹ ,
王飏 ² ,
姚美萍 ²

作者信息 +

^1. 晋中学院数学系，山西晋中 030619

^2. 山西大学数学与统计学院，山西太原 030006

石玲玲（1989 $-$ ），女，山西临汾人，硕士，讲师，研究方向为微分方程和动力系统。E-mail：sll@jzxy.edu.cn

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Traveling Wave Solutions for Mixed Diffusive Competition Systems with Spatio-temporal Delays

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摘要

本文主要研究一类带有时空时滞的混合扩散竞争系统行波解的存在性。首先，为了消除时空时滞的影响，根据时空时滞中核函数的特性，把带有时空时滞的由两个方程耦合而成的扩散系统转化为无时滞的由四个方程耦合而成的扩散系统。其次，通过变换将系统转化为单调系统。最后，利用上下解方法和不动点定理证明行波解的存在性。

关键词

反应扩散系统 / 上下解 / 非局部时滞

Key words

reaction diffusion system / super- and sub-solutions / nonlocal delays

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