强耦合捕食系统古典解的存在性

Existence of Classical Solutions to a Strongly Coupled Predator-Prey Model

研究了在Neumann边界条件及反应函数功能性Ⅱ下带有自扩散和食饵趋向的捕食系统.对食饵趋向引入"Volume-Filling"机制,引入函数的Banach空间,定义了范数.应用压缩原理,H·lder连续,抛物方程Schauder估计及Lp估计,证明了此系统古典解的局部存在唯一性,并对其建立了先验估计,再把局部解延拓为全局解.

Predator-prey model with self-diffusion and prey-taxis incorporating Holling type Ⅱ functional response was dealt with under homogeneous Neumann boundary condition.＂volume-filling＂ mechanism and Banach space were introduced,norm was defined.By applying the contraction mapping principle,the H·lder continuity,the parabolic Schauder estimates and parabolic Lp estimates,it proves that there exists a unique global classical solution of this system and establishs a priori estimate,then extends the local solution to a global solution.