奇摄动时滞反应扩散方程

莫嘉琪; 温朝晖

doi:10.3879/j.issn.1000-0887.2010.06.011

奇摄动时滞反应扩散方程

doi: 10.3879/j.issn.1000-0887.2010.06.011

莫嘉琪^1,2,
温朝晖³

安徽师范大学数学系,安徽芜湖 241000;2.上海高校计算科学E-研究院 SJTU研究所, 上海 200240;3.安徽财经大学统计与应用数学学院应用数学研究所, 安徽蚌埠 233030

基金项目: 国家自然科学基金资助项目(40876010);中国科学院知识创新工程重要方向资助项目(KZCX2-YW-Q03-08);公益性行业科研专项资助项目(GYHY200806010);LASG国家重点实验室专项经费资助项目;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(Y6090164)

详细信息

作者简介:
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: O175.29
计量
- 文章访问数: 1655
- HTML全文浏览量: 101
- PDF下载量: 777
- 被引次数: 0
出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2010-05-10
- 刊出日期: 2010-06-15

Singularly Perturbed Reaction Diffusion Equations With Time Delay

MO Jia-qi^1,2,
WEN Zhao-hui³

Department of Mathematics, Anhui Normal University, Wuhu, Anhui 241000, P. R. China;

摘要

摘要: 研究了一类带有小延迟的微分-差分反应扩散方程初值边值问题．在适当的条件下，利用伸长变量法，构造了问题的形式渐近解．再用微分不等式理论证明了解的一致有效性．
- 非线性 /
- 反应扩散 /
- 奇摄动 /
- 时滞
Abstract: A class of differential difference reaction diffusion equations initial boundary problem with a small time delay was considered. Under suitable conditions and by using method of the stretched variable, the formal asymptotic solution was constructed. And then, by using the theory of differential inequalities, the uniformly validity of solution was proved.
- non linear /
- reaction diffusion /
- singular perturbation /
- time delay

HTML全文

参考文献(21)

[1]	Barbu L, Morosanu. Singularly Perturbed Boundary-Value Problems[M]. Basel: Birkhauserm Verlag AG, 2007.
[2]	Ni W M, Wei J C. On positive solution concentrating on spheres for the Gierer-Meinhardt system[J]. J Diff Eqns， 2006, 221(1): 158-189. doi: 10.1016/j.jde.2005.03.004
[3]	Alfaro M, Hilhorst D, Matano H. The singular limit of the Allen-Cahn equation and the FitzHugh-Nagumo system[J]. J Diff Eqns, 2008, 245(2): 505-565 . doi: 10.1016/j.jde.2008.01.014
[4]	Khasminskii R Z, Yin G. Limit behavior of two-time-scale diffusion revisited[J]. J Diff Eqns, 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 Diff Eqns, 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 Sin, 2005, 21(1): 101-104. doi: 10.1007/s10255-005-0220-4
[10]	MO Jia-qi, LIN Wan-tao. Asymptotic solution of activator inhibitor systems for nonlinear reaction diffusion equations[J]. J Sys Sci Complexity, 2008, 20(1): 119-128.
[11]	MO Jia-qi, Shao S. The singularly perturbed boundary value problems for higher-order semi-linear elliptic equations[J]. Advances in Math, 2001, 30(2): 141-148.
[12]	Mo J Q, Zhu J, Wang H. Asymptotic behavior of the shock solution for a class of nonlinear equations[J]. Progress in Natural Science, 2003, 13(9): 768-770. doi: 10.1080/10020070312331344400
[13]	莫嘉琪，张伟江，陈贤峰. 强非线性发展方程孤波同伦解法[J]. 物理学报, 2007, 56(11): 6169-6172.
[14]	莫嘉琪，张伟江，何铭. 激光脉冲放大器传输波的计算[J]. 物理学报, 2006, 55(7): 3233-3236.
[15]	Mo J Q, Wang H, Lin W T. Varitional iteration solving method for El-Nio phenomenon atmpspheric physics of nonlinear model[J]. Acta Oceanol Sin, 2005, 24(5): 35-38.
[16]	MO Jia-qi, LIN Wan-tao, WANG Hui. Variational iteration method for solving perturbed mechanism of western boundary undercurrents in the Pacific[J]. Chin Phys, 2007, 16(4): 951-964. doi: 10.1088/1009-1963/16/4/016
[17]	MO Jia-qi, LIN Wan-tao, WANG Hui. Variational iteration solving method of a sea-air oscillator model for the ENSO[J]. Prog Nat Sci, 2007, 17(2): 230-232. doi: 10.1080/10020070612331343252
[18]	MO Jia-qi, WANG Hui, LIN Wan-tao, LIN Yi-hua. Varitional iteration method for 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
[19]	MO Jia-qi, LIN Wan-tao, WANG Hui. Variational iteration method for solving perturbed mechanism of western boundary undercurrents in the Pacific[J]. Chin Phys, 2007, 16(4): 951-964. doi: 10.1088/1009-1963/16/4/016
[20]	MO Jia-qi, LIN Wan-tao. Asymptotic solution for a class of sea-air oscillator model for El-Nio-southern oscillation[J]. Chin Phys, 2008, 17(2): 370-372. doi: 10.1088/1674-1056/17/2/002
[21]	Pao C V. Comparison methods and stability analysis of reaction diffusion systems[C]LIU Xin-zhi.Lecture Notes in Pure Appl Math,162. New York:Marcel Dekker Inc, 1994:277-292.