一个含对流项的反应扩散捕食模型正解的存在性  

Existence of positive solutions of a reaction-diffusion predator model with advection term

作　　者：高歌 董亚莹 GAO Ge;DONG Ya-Ying(College of Science,Xi'an Polytechnic University,Xi'an 710048,China)

机构地区：[1]西安工程大学理学院,西安710048

出　　处：《四川大学学报（自然科学版）》2024年第1期44-50,共7页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11801431);陕西省高校科协青年人才托举计划(20190509);陕西省自然科学基金(2023-JC-YB-038)。

摘　　要：本文研究了一个含对流项的反应扩散捕食模型正解的存在性,该模型描述了两物种间的捕食关系及捕食者选择在远离高密度食饵区域捕猎的倾向.基于模型正解的先验估计,本文利用特征值理论和齐次化理论获得了模型正解关于两物种增长率的不存在性,然后利用分歧理论获得了模型正解在某些参数条件下的存在性.In this paper,we focus on the existence of positive solutions of a reaction-diffusion predator model with advection term.This model can be used to describe the relationship between the predator species and the prey species with a tendency that predators choose to hunt away from the high-density area of prey species.Based on a priori estimate for positive solutions,the non-existence of positive solutions with respect to the growth rate of both species is established by using the eigenvalue theory and homogenization theory.Then the existence of positive solutions for different parameter conditions is established by using the bifurcation theory.

关 键 词：反应扩散捕食模型 全局分岔 先验估计 

分 类 号：O175[理学—数学] Q141[理学—基础数学]