| 一类带交叉扩散项的Variable-Territory捕食-食饵模型 |
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| 引用本文： | 董苗娜,容跃堂,王晓丽,殷珍杰. 一类带交叉扩散项的Variable-Territory捕食-食饵模型[J]. 纺织高校基础科学学报, 2017, 30(1). DOI: 10.13338/j.issn.1006-8341.2017.01.009 |
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| 作者姓名： | 董苗娜 容跃堂 王晓丽 殷珍杰 |
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| 作者单位： | 西安工程大学理学院,陕西西安,710048 |
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| 基金项目： | 陕西省自然科学基础研究计划项目 |
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| 摘 要： | 在齐次Dirichlet边界条件下,研究一类带交叉扩散项的Variable-Territory捕食-食饵模型正解的存在性问题.通过利用极大值原理和分歧理论给出对应的平衡态方程正解的先验估计以及局部分歧正解的存在性条件,并且将局部分歧解延拓为全局分歧解.结果表明,在一定条件下,捕食者和食饵是可以共存的.
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| 关 键 词： | 捕食-食饵 交叉扩散 正解 全局分歧 |
A class of prey-predator model with cross-diffusion and variable-territory type |
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| DONG Miaona,RONG Yuetang,WANG Xiaoli,YIN Zhenjie. A class of prey-predator model with cross-diffusion and variable-territory type[J]. Basic Sciences Journal of Textile Universities, 2017, 30(1). DOI: 10.13338/j.issn.1006-8341.2017.01.009 |
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| Authors: | DONG Miaona RONG Yuetang WANG Xiaoli YIN Zhenjie |
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| Abstract: | Under homogeneous Dirichlet boundary conditions,the existence of positive solutions for a predator-prey model with Variable-Territory type and cross-diffusion is researched.By the maximum principle and Crandall-Rabinowitz bifurcation theory,a priori estimate of positive solutions are obtained and the existence of positive solutions to a local bifurcation is proved.Finally,the local bifurcation is developed to the global one,which shows that the predator and the prey can coexist under certain conditions. |
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| Keywords: | predator-prey model cross-diffusion positive solution global bifurcation |
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