一类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

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，然后利用分岔理论获得了模型正解在某些参数条件下的存在性.

Abstract:

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 pecies with the tendency that predators choose to hunt away from the high-density area of prey species. Based on a priori estimate for the positive solutions, the non-existence of positive solutions with respect to the growth rate of both species is estabished 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.