| 三种群食物链交错扩散模型的整体 |
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| 引用本文： | 伏升茂(),温紫娟(),崔尚斌(. 三种群食物链交错扩散模型的整体[J]. 数学学报, 2007, 50(1): 75-88 |
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| 作者姓名： | 伏升茂() 温紫娟() 崔尚斌( |
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| 作者单位： | [1]西北师范大学数学与信息科学学院,兰州730070 [2]中山大学数学系,广州510275 |
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| 基金项目： | 国家自然科学基金资助项目（10471157）;甘肃省自然科学基金资助项目（3ZS061-A25-015） |
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| 摘 要： | 本文应用能量估计方法和Gagliardo-Nirenberg型不等式证明了一类强耦合反应扩散系统整体解的存在性和一致有界性，该系统是带自扩散和交错扩散项的三种群Lotka-Volterra食物链模型．通过构造Lyapunov函数给出了该模型正平衡点全局渐近稳定的充分条件．
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| 关 键 词： | 自扩散 交错扩散 整体解 一致 |
| 文章编号： | 0583-1431（2007）01-0075-14 |
| 收稿时间： | 2005-01-14 |
| 修稿时间： | 2005-01-14 |
On Global Solutions for the Th |
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| Sheng Mao FU ,Zi Juan WEN,Shang Bin CUI. On Global Solutions for the Th[J]. Acta Mathematica Sinica, 2007, 50(1): 75-88 |
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| Authors: | Sheng Mao FU Zi Juan WEN Shang Bin CUI |
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| Affiliation: | 1.College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, P. R. China;2.Department of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China |
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| Abstract: | Using the energy estimate and Gagliardo-Nirenberg-type inequalities, the existence and the uniform boundedness of global solutions for a strongly coupled reactiondiffusion system are proved. This system is the Lotka Volterra food chain model of three interacting species with self and cross-population pressure. Meanwhile, the sufficient condition for global asymptotic stability of the positive equilibrium point for the model is given by constructing the Lyapunov function. |
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| Keywords: | self-diffusion cross-diffusion global solutions |
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