| 一类捕食-被捕食控制反应扩散方程非线性奇摄动问题 |
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| 引用本文： | 莫嘉琪,谢峰. 一类捕食-被捕食控制反应扩散方程非线性奇摄动问题[J]. 生物数学学报, 2006, 21(1): 1-8 |
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| 作者姓名： | 莫嘉琪 谢峰 |
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| 作者单位： | 1. 湖州师范学院,数学系,浙江,湖州,313000;上海高校计算科学E-研究院上海交通大学研究所,上海,200240
2. 上海高校计算科学E-研究院上海交通大学研究所,上海,200240;东华大学,应用数学系,上海,201620 |
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| 基金项目： | Supported by the National Natural Science Foundation of China (90111011 and 10471039)the National Key Project for Basics Research (2003CB415101-03 and 2004CB418304)the Key Project of the Chinese Academy of Sciences (KZCX3-SW-221)in part by E-Insitutes of Shanghai Municipal Education Commission (N.E03004) |
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| 摘 要： | 研究了一类非线性反应扩散方程奇摄动问题．在适当的条件下,首先求出了原问题的外部解, 然后利用伸长变量和幂级数展开理论构造出解的形式渐近展开式．最后利用微分不等式理论,讨论了问题解的一致有效性和渐近性态．
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| 关 键 词： | 非线性 反应扩散 奇摄动 捕食-被捕食 |
| 文章编号： | 1001-9626（2006）01-0001-08 |
| 收稿时间： | 2004-03-10 |
| 修稿时间： | 2004-03-10 |
A Class of Nonlinear Singularly Perturbed Problems for Predator-Prey Control Reaction Diffusion Equations |
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| MO Jia-qi,XIE Feng. A Class of Nonlinear Singularly Perturbed Problems for Predator-Prey Control Reaction Diffusion Equations[J]. Journal of Biomathematics, 2006, 21(1): 1-8 |
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| Authors: | MO Jia-qi XIE Feng |
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| Affiliation: | 1 Department of Mathematics, Huzhou Teachers College, Huzhou Zhejiang 313000 China;2 Division of Computational Science, E - Institutes of Shanghai Universities at SJTU, Shanghai 200240 China;3 Department of Applied Mathematics, Donghua University, Shanghai 201620 China |
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| Abstract: | A class of nonlinear singularly perturbed problems for predator-prey reaction diffusion equations is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the stretched variable, variables of multiple scales and the expanding theory of power series the formal asymptotic expansions of the solution is constructed, and finally, using the theory of differential inequalities the uniform validity and asymptotic behavior of the solution are studied. |
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| Keywords: | nonlinear Reaction diffusion Singular perturbation Predator-pery |
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