带有交叉扩散项的Gause型捕食-食饵模型的共存态  

Stationary Partterns of Gause-Type Prey-Predator Model with Diffusion and Cross-Diffusion

作　　者：王珊珊[1] 李艳玲[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《安徽师范大学学报（自然科学版）》2011年第6期527-532,共6页Journal of Anhui Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(10971124);教育部高等学校博士点专项资助项目(200807180004)

摘　　要：研究了带有交叉扩散项的Gause型捕食-食饵模在齐次Neumann边界条件下的非常数正解的存在性.首先利用最大值原理和Harnack不等式对正解的上下界做了先验估计;其次利用积分性质讨论了非常数正解的不存在性;最后在先验估计的基础上运用Leray-Schauder度理论证明了非常数正解的存在性.A Gause-type predator-prey model with diffusion and cross-diffusion under homogeneous Neumann boundary condition are investigated. First, by means of the maximum principle and Harnack inequality, a priori estimate for upper and lower bounds is discussed. Second, by using the intergral property, the non-existence of the non-constant postive solusion is studied. Third, the existence of steady-state solutions is proved by the priori upper and lower bounds and Leray-Schuder degree theory.

关 键 词：捕食-食饵模型 交叉扩散 正解 Leray—Schauder度理论 

分 类 号：O175.26[理学—数学]