具有双参数的弱非线性方程的奇摄动解

陈丽华; 莫嘉琪

具有双参数的弱非线性方程的奇摄动解

陈丽华¹,
莫嘉琪^2,3

1.
福建师范大学福清分校数学与计算机科学系,福建福涛 350300;2.上海高校计算科学E_研究院SJTU研究所,上海 200240;3.湖州师范学院数学系,浙江湖州 313000

基金项目: 国家自然科学基金项目(40676016,10471039);国家重点基础研究发展规划项目(2003CB415101-032004CB418304);中国科学院知识创新工程方向性资助项目(KZCX3-SW-221);上海市教育委员会E-研究院建设计划资助项目(E03004);浙江省自然科学基金资助项目(Y606268)

详细信息

作者简介:
陈丽华(1962- ),女,福建福清人,副教授(Tel:+86-591-85286697;E-mail:clhfq@yahoo.com.cn);莫嘉琪(1937- ),男,浙江德清人,教授(联系人.Tel:+86-553-3869642;E-mail:mojiaqi@mail.ahnu.edu.cn).

中图分类号: O175.14
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出版历程
- 收稿日期: 2007-01-16
- 修回日期: 2007-08-08
- 刊出日期: 2007-10-15

Singularly Perturbed Soluton for Weakly Nonlinear Equations With Two Parameters

CHEN Li-hua¹,
MO Jia-qi^2,3

1.
Department of Mathematics and Computer Science, Fuqing Branch of Fujian Normal University, Fuqing, Fujian 350300, P. R. China;

摘要

摘要: 讨论了一四阶具有双参数的弱非线性方程在有限区间上的奇摄动边值问题．在一定的假设下，首先，利用幂级数形式展开方法，构造了原问题的外部解A·D2其次，利用伸长变量，在左端点附近构造问题解的第一边界层校正项．然后，利用更强的伸长变量，仍然在左端点附近构造问题解的第二边界层校正项．第二边界层的厚度比第一边界层的厚度更小，形成在左端点附近的边界层的套层．最后利用微分不等式理论，证明了边值问题解的存在性、和在整个区间内一致有效性和渐近性态，得到了满意的结果．
- 非线性 /
- 两参数 /
- 奇摄动
Abstract: A class of singularly perturbed boundary value problem of weakly nonlinear equation for fourth order on the finite interval with two parameters is considered.Under suitable conditions,firstly,using the expansion method of power series,the reduced solution and formal outer solution are constructed.Secondly,using the transformation of stretched variable,the first boundary layer corrective term near the left endpoint is constructed which possesses exponential attenuation behavior.And then,using the stronger transformation of stretched variable,the second boundary layer corrective term near the left endpoint is constructed too,which also possesses exponential attenuation behavior.The thickness of second boundary layer smaller than first boundary layer and forms the cover layer near the left endpoint.Finally,using the theory of differential inequalities the existence,uniform validity in the whole interval and asymptotic behavior of solution for the original boundary value problem are proved.The satisfying results are obtained.
- nonlinear /
- two parameters /
- singular perturbation

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参考文献(16)

[1]	de Jager E M,JIANG Fu-ru.The Theory of Singular Perturbation[M].Amsterdam: North-Holland Publishing Co,1996.
[2]	NI Wei-ming,WEI Jun-cheng.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
[5]	Marques I. Existence and asymptotic behavior of solutions for a class of nonlinear elliptic equations with Neumann condition[J].Nonlinear Anal,2005,61(1):21-40. doi: 10.1016/j.na.2004.11.006
[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]	莫嘉琪，朱江.非线性非局部反应扩散方程奇摄动问题[J].应用数学和力学，2003,24(5):446-470.
[10]	莫嘉琪，王辉，林万涛.一类具有边界摄动的非线性非局部反应扩散方程奇摄动问题[J].应用数学和力学，2005,26(12):1507-1510.
[11]	MO Jia-qi,Shao S.The singularly perturbed boundary value problems for higher-order semilinear elliptic equations[J].Advances in Math,2001,30(2):141-148.
[12]	莫嘉琪，王辉.一类非线性奇摄动问题激波位置的转移[J].应用数学和力学，2005,26(1):53-57.
[13]	MO Jia-qi,LIN Wan-tao,ZHU Jiang.A variational iteration solving method for ENSO mechanism[J].Progress in Natural Science,2004,14(12):1126-1128. doi: 10.1080/10020070412331344921
[14]	MO Jia-qi,WANG Hui,LIN Wan-tao,et al.Sea-air oscillator model for equatorial eastern Pacific SST[J].Acta Phys Sinica,2006,55(1):6-9.
[15]	MO Jia-qi,WANG Hui,LIN Wan-tao,et al.Variational iteration method the mechanism of the equatorial eastern Pacific El Nino-Southern oscillation[J].Chin Phys,2006,15(4):671-675. doi: 10.1088/1009-1963/15/4/003
[16]	O'Malley R E.Introduction to Singular[M].New York: Academic Press, 1974.

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具有双参数的弱非线性方程的奇摄动解

作者简介:
陈丽华(1962- ),女,福建福清人,副教授(Tel:+86-591-85286697;E-mail:clhfq@yahoo.com.cn);莫嘉琪(1937- ),男,浙江德清人,教授(联系人.Tel:+86-553-3869642;E-mail:mojiaqi@mail.ahnu.edu.cn).

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Singularly Perturbed Soluton for Weakly Nonlinear Equations With Two Parameters

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留言板

具有双参数的弱非线性方程的奇摄动解

作者简介: 陈丽华(1962- ),女,福建福清人,副教授(Tel:+86-591-85286697;E-mail:clhfq@yahoo.com.cn);莫嘉琪(1937- ),男,浙江德清人,教授(联系人.Tel:+86-553-3869642;E-mail:mojiaqi@mail.ahnu.edu.cn).

计量

出版历程

Singularly Perturbed Soluton for Weakly Nonlinear Equations With Two Parameters

计量

出版历程

目录

作者简介:
陈丽华(1962- ),女,福建福清人,副教授(Tel:+86-591-85286697;E-mail:clhfq@yahoo.com.cn);莫嘉琪(1937- ),男,浙江德清人,教授(联系人.Tel:+86-553-3869642;E-mail:mojiaqi@mail.ahnu.edu.cn).