捕食-被捕食反应扩散方程非线性奇摄动问题(英文) 被引量：1

The Nonlinear Singularly Perturbed Problems for Predator-Prey Reaction Diffusion Equations

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摘要研究了非线性反应扩散方程奇摄问题.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. The 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 and the expanding theory of power series the formal asymptotic expansion of the solution is constructed, and finally, using the theory of differential inequalities the uniform validity and asymptotic behavior of the solution are studied.

作者欧阳成莫嘉琪

机构地区湖州师范学院

出处《生物数学学报》 CSCD 北大核心 2005年第2期135-141,共7页 Journal of Biomathematics

基金 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) the Natural Science Foundation of Zhejiang Province(l02009)

关键词非线性反应扩散奇摄动 Nonlinear Reaction diffusion Singular perturbation

分类号 O175.29 [理学—基础数学]

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参考文献5

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二级参考文献17

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共引文献301

1欧阳成,莫嘉琪.一个非线性方程转向点问题[J].应用数学,2001,14(2):6-7. 被引量：8
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3Yao Jingsun, Mo Jiaqi (Dept. of Math., Anhui Normal University, Wuhu 241000, Anhui,Division of Computational Science, E-Institutes of Shanghai Universities, at SJTU, Shanghai 200240).SINGULARLY PERTURBED SOLUTION TO SEMILINEAR HIGHER ORDER REACTION DIFFUSION EQUATIONS WITH TWO PARAMETERS[J].Annals of Differential Equations,2009,25(1):91-96. 被引量：1
4冯茂春.一类微分方程激波解的多层现象[J].杭州师范学院学报（自然科学版）,2003,2(1):12-15.
5莫嘉琪.具有奇性方程的非线性奇摄动问题的正解(英文)[J].应用数学,2010(1):13-17. 被引量：1
6MO Jiaqi and WANG Hui(1. Anhui Normal University, Wuhu 241000, China,2. National Natural Science Foundation of China, Beijing 100085, China).Shock solution for quasilinear singularly perturbed Robin problem[J].Progress in Natural Science:Materials International,2002,12(12):945-947. 被引量：70
7LIU,Qi-lin(刘其林),MO,Jia-qi(莫嘉琪).THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR THE SINGULARLY PERTURBED INITIAL BOUNDARY VALUE PROBLEMS OF THE REACTION DIFFUSION EQUATIONS IN A PART OF DOMAIN[J].Applied Mathematics and Mechanics(English Edition),2001,22(10):1192-1197. 被引量：1
8Liu Shude~1 Chen Lihua~2 Mo Jiaqi~(1,3) (1.Dept.of Math.,Anhui Normal University,Wuhu 241000,Anhui,2.Dept.of Math.,Fuqing Branch of Fujian Normal University,Fuqing 350300,Fujian,3.Division of Computational Science,E-Institutes of Shanghai Universities,at SJTU,Shanghai 200240).THE INITIAL-BOUNDARY VALUE PROBLEMS OF NONLINEAR AND NONLOCAL SINGULARLY PERTURBED REACTION DIFFUSION SYSTEM[J].Annals of Differential Equations,2008,24(1):20-28. 被引量：5
9Mo Jiaqi1,2,Yao Jingsun1(1. Dept. of Math.,Anhui Normal University,Wuhu 241000,Anhui,2. Division of Computational Science,E-Institutes of Shanghai Universities at SJTU,Shanghai 200240).THE GENERALIZED FUNCTIONAL-VARIATION SOLVING METHODS FOR NONLINEAR REACTION DIFFUSION IN BIONOMICS OF SPECIES GROUPS[J].Annals of Differential Equations,2008,24(2):193-196. 被引量：1
10Jingsun Yao, Jiaqi Mo (Dept. of Math., Anhui Normal University, Wuhu 241000, Anhui,Division of Computational Science, E-Institutes of Shanghai Universities, at SJTU, Shanghai 200240).ASYMPTOTIC SOLUTION TO NONLINEAR REACTION DIFFUSION EQUATION WITH TWO SMALL PARAMETERS[J].Annals of Differential Equations,2010,26(1):100-104.