具有边界摄动弱非线性反应扩散方程的奇摄动

莫嘉琪

具有边界摄动弱非线性反应扩散方程的奇摄动

莫嘉琪^1,2,3

1.
安徽师范大学数学系,安徽芜湖 241000;2.湖州师范学院数学系,浙江湖州 313000;3.上海高校计算科学E_研究院上海交通大学研究所,上海 200240

基金项目: 国家自然科学基金资助项目(40676016;10471039);国家重点基础研究发展规划项目(2003CB415101-03;2004CB418304);中国科学院知识创新工程方向性项目(KZCX3-SW-221);上海市教育委员会E-研究院建设计划项目(NE03004)

详细信息

作者简介:
莫嘉琪(1937- ),男,浙江德清人,教授(Tel:+86-553-3869642;E-mail:mojiaqi@mail.ahnu.edu.cn).

中图分类号: O175.29
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- 文章访问数: 2817
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出版历程
- 收稿日期: 2007-03-21
- 修回日期: 2008-07-02
- 刊出日期: 2008-08-15

Singular Perturbation for the Weakly Nonlinear Reaction Diffusion Equation With Boundary Perturbation

MO Jia-qi^1,2,3

1.
Anhui Normal University, Wuhu, Anhui 241000, P. R. China;

摘要

摘要: 在适当的条件下研究了一类具有边界摄动的非线性反应扩散方程奇摄动初始边值问题．首先，借助正规摄动方法，得到了原问题的外部解．其次，利用伸长变量和幂级数展开理论，构造了解的初始层项．然后，利用微分不等式理论，研究了初始边值问题解的渐近性态．最后，利用一些相关的不等式，讨论了原问题解的存在、唯一性及其一致有效的渐近估计．
- 非线性 /
- 反应扩散 /
- 奇摄动 /
- 边界摄动
Abstract: A class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation is considered under suitable conditions.Firstly,by dint of regular perturbation method,the outer solution of the original problem was obtained.Secondly,by using the stretched variable and the expanding theory of power series,the initial layer term of solution was constructed.And then,by using the theory of differential inequalities the asymptotic behavior of solutions for the initial boundary value problems was studied.finally,using some relational inequalities the existence and uniqueness of solution for the original problem and the uniforntly valid asympfolic estimation were discussed.
- nonlinear /
- reaction diffusion /
- singular perturbation /
- boundary perturbation

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参考文献(20)

[1]	de Jager E M, Jiang F R.The Theory of Singular Perturbation[M].Amsterdam:North-Holland Publishing Co,1996.
[2]	Ni W M，Wei J C. On positive solution concentrating on spheres for the Gierer-Meinhardt system[J].J Differential Equations，2006,221(1):158-189. doi: 10.1016/j.jde.2005.03.004
[3]	Zhang F. Coexistence of a pulse and multiple spikes and transition layers in the standing waves of a reaction-diffusion system[J].J Differential Equations,2004,205(1):77-155. doi: 10.1016/j.jde.2004.06.017
[4]	Khasminskii R Z, Yin G.Limit behavior of two-time-scale diffusion revisited[J].J Differential Equations,2005,212(1):85-113. doi: 10.1016/j.jde.2004.08.013
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[6]	Bobkova A S. The behavior of solutions of multidimensional singularly perturbed system with one fast variable[J].J Differential Equations,2005,41(1):23-32.
[7]	MO Jia-qi. A singularly perturbed nonlinear boundary value problem[J].J Math Anal Appl,1993,178(1):289-293. doi: 10.1006/jmaa.1993.1307
[8]	MO Jia-qi.Singular perturbation for a class of nonlinear reaction diffusion systems[J].Science in China, Ser A,1989,32(11):1306-1315.
[9]	MO Jia-qi,LIN Wan-tao.A nonlinear singular perturbed problem for reaction diffusion equations with boundary perturbation[J].Acta Math Appl Sinica,2005,21(1):101-104. doi: 10.1007/s10255-005-0220-4
[10]	MO Jia-qi, Shao Salley.The singularly perturbed boundary value problems for higher-order semilinear elliptic equations[J].Advances in Math,2001,30(2):141-148.
[11]	MO Jia-qi, ZHU Jiang,WANG Hui. Asymptotic behavior of the shock solution for a class of nonlinear equations[J].Progress in Natural Sci,2003,13(9):768-770. doi: 10.1080/10020070312331344400
[12]	MO Jia-qi, LIN Wan-tao,ZHU Jiang. A variational iteration solving method for ENSO mechanism[J].Progress in Natural Sci,2004,14(12):1126-1128. doi: 10.1080/10020070412331344921
[13]	MO Jia-qi, WANG Hui,LIN Wan-tao.Varitional iteration solving method for El Nino phenomenon atmpspheric physics of nonlinear model[J].Acta Oceanol Sinica,2005,24(5):35-38.
[14]	MO Jia-qi, WANG Hui,LIN Wan-tao.Singularly perturbed solution of a sea-air oscillator model for the ENSO[J].Chin Phys,2006,15(7):1450-1453. doi: 10.1088/1009-1963/15/7/011
[15]	MO Jia-qi, WANG Hui,LIN Wan-tao,et al.Varitional iteration method foe solving the mechanism of the equatorial Eastern Pacific El Nio-Southern Oscillation[J].Chin Phys,2006,15(4):671-675. doi: 10.1088/1009-1963/15/4/003
[16]	莫嘉琪，王辉，林万涛.厄尔尼诺-南方涛动时滞海-气振子耦合模型[J].物理学报,2006,55(7):3229-3232.
[17]	MO Jia-qi, WANG Hui. A class of nonlinear nomlocal singularly perturbed problems for reaction diffusion equations[J].J Biomathematics,2002,17(2):143-148.
[18]	莫嘉琪. HIV传播人群生态动力学模型[J].生态学报,2006,26(1):104-107.
[19]	Protter M H, Weinberger H F.Maximum Principles in Differential Equations[M].New York: Prentice-Hall Inc,1967.
[20]	Pao C V. Comparison methods and stability analysis of reaction diffusion systems[J].Lecture Notes in Pure and Appl Math,1994,162(1):277-292.

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文章访问数: 2817
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具有边界摄动弱非线性反应扩散方程的奇摄动

作者简介:
莫嘉琪(1937- ),男,浙江德清人,教授(Tel:+86-553-3869642;E-mail:mojiaqi@mail.ahnu.edu.cn).

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Singular Perturbation for the Weakly Nonlinear Reaction Diffusion Equation With Boundary Perturbation

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留言板

具有边界摄动弱非线性反应扩散方程的奇摄动

作者简介: 莫嘉琪(1937- ),男,浙江德清人,教授(Tel:+86-553-3869642;E-mail:mojiaqi@mail.ahnu.edu.cn).

计量

出版历程

Singular Perturbation for the Weakly Nonlinear Reaction Diffusion Equation With Boundary Perturbation

计量

出版历程

目录

作者简介:
莫嘉琪(1937- ),男,浙江德清人,教授(Tel:+86-553-3869642;E-mail:mojiaqi@mail.ahnu.edu.cn).