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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
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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.
作者 王珊珊 李艳玲
机构地区 陕西师范大学数学与信息科学学院
出处 《安徽师范大学学报（自然科学版）》 CAS 北大核心 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)
关键词 捕食-食饵模型 交叉扩散 正解 Leray—Schauder度理论 prey-predator cross diffusion postive solution Leray-Schauder degree theory
分类号 O175.26 [理学—基础数学]
  • 相关文献

参考文献8

  • 1KUANG Yang, FREEDMAN HI. Uniqueness of limit cycles in gause-typemodel of preclator-preysystems[J]. Mathematical Biosciences 1998,88:67 -84.
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二级参考文献6

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共引文献3

安徽师范大学学报（自然科学版）
2011年 第6期

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