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

作　　者：李成林[1,2] 

机构地区：[1]西南大学数学与统计学院,重庆400715 [2]保山学院数学学院,云南保山678000

出　　处：《中北大学学报（自然科学版）》2013年第2期98-102,108,共6页Journal of North University of China(Natural Science Edition)

基　　金：国家教育部自然科学基金资助项目(XDJK2009C152)

摘　　要：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.

关 键 词：古典解 H·lder连续 SCHAUDER估计 Lp估计 

分 类 号：O175.1[理学—数学]