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singular perturbation for the weakly nonlinear reaction diffusion equation with boundary perturbation

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Applied Mathematics and Mechanics(English Edition) 2008年第8期29卷 1105-1110页

作者： MO Jia-qi Department of Mathematics Anhui Normal University Wuhu 241000 Anhui Province P. R. China Department of Mathematics Huzhou Teachers College Huzhou 313000 Zhejiang Province P. R. China Division of Computational Science E-Institutes of Shanghai Universities at Shanghai Jiaotong University Shanghai 200240 P. R. China

In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the regular perturbation method, the outer solution of the original problem is obtained. Secondly, by using the stretched variable and the expansion theory of power series the initial layer of the solution is constructed. And then, by using the theory of differential inequalities, the asymptotic behavior of the solution for the initial boundary value problems is studied. Finally, using some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.

关键词： nonlinear reaction diffusion singular perturbation boundary perturbation

singular perturbation OF BOUNDARY VALUE PROBLEM FOR QUASILINEAR THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS INVOLVING TWO SMALL PARAMETERS

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Applied Mathematics and Mechanics(English Edition) 2001年第2期22卷 229-236页

作者：林苏榕田根宝林宗池 Mathernatical Section Fujian Broadcasting TV University Fuzhou 350003 P R China Department of Mathematics S hanghai Railroad University S hanghai 200333 P R China Department of Mathernatics Fujian Normal University Fuzhou 350007 P R China

The singularly perturbed boundary value problem for quasilinear third-order ordinary differential equation involving two small parameters has been considered. For the three cases epsilon/mu (2) --> 0(mu --> 0), mu (2)/epsilon --> 0(epsilon --> 0) and epsilon = mu (2), the formal asymptotic solutions are constructed by the method of two steps expansions and the existences of solution are proved by using the differential inequality method. In addition, the uniformly valid estimations of the remainder term are given as well.

关键词： two-parameters singular perturbation boundary value problem asymptotic expansion

singular perturbation OF THE FOURTH ORDER ELLIPTIC EQUATION WHEN THE LIMIT EQUATION IS ELLIPTIC-PARABOLIC

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Applied Mathematics and Mechanics(English Edition) 1991年第1期12卷 77-84页

作者：林宗池 Department of Mathematics Fujian Normal University Fuzhou

This paper considers the singular perturbation of a fourth order elliptic equation when the limit equation is elliptic-parabolic. The equation involves a positive parameter, a positive real number, a Laplacian operator, and sufficient smoothness. Under appropriate condition the sufficient condition of solvability is derived, the existence of solution is proved and a uniformly valid asymptotic solution of arbitrary order is given.

关键词： singular perturbation limit equation elliptic equation

singular perturbation OF SECOND-ORDER NONLINEAR SYSTEM WITH BOUNDARY perturbation

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Applied Mathematics and Mechanics(English Edition) 2000年第2期21卷 227-236页

作者：陈育森 Department of Mathematics Fuqing Brach Fujian Normal University Fuqing P R China

The singular perturbation of boundary value problem of second-order nonlinear system of differential equations with integral operators and boundary perturbation is discussed. Under the suitable assumed conditions, by ... 详细信息

关键词： singular perturbation boundary perturbation diagonalization

singular　perturbation　FOR　A　NONLINEAR　BOUNDARY　VALUE　PROBLEM　OF　FIRST　ORDER　SYSTEM

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Applied Mathematics and Mechanics(English Edition) 1996年第11期17卷 1095-1100页

作者：陈松林 East China Institute of Metallurgy Maanshan P. R. China

In this paper, we study the following perturbed nonlinear boundary value problemof the form:εx' =f(t, x,y, ε)εy' =g(t, x,y, ε)x(0)= A(ξ1,ξ2 ,x(1) -x(0), y(1 )- y(0), ε)y(0)=B(ξ1, ξ2,x(1)-￣x(0 ),y(1 )-g(0 ),ε)where ξ1, ξ2 are functions of ε. 0<ε<<1. Under some suitable conditions, we give the asymptotic expansion of solution of any order, and obtain the estimation of remaindet term by using the comparison theorem.

关键词： nonlinear boundary value singular perturbation comparisontheorem asymptotic expansion

singular perturbation FOR REACTION DIFFUSION EQUATIONS

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Applied Mathematics(A Journal of Chinese Universities) 2003年第3期18卷 251-257页

作者： MoJiaqi WangHui ZhuJiang Dept.ofMath. HuzhouTeachersCollegeHuzhou313000China. CommitteeofNationalNaturalSciencesFoundationofChina Beijing100085China. ICEES InstituteofAtmosphericPhysicsChineseAcademyofSciencesBeijing100029China.

The singularly perturbed initial boundary value problems for reaction diffusion equations are *** suitable conditions and by using the theory of differential inequality,the asymptotic behavior of solution for initial ... 详细信息

关键词： nonlinear reaction diffusion equation singular perturbation

singular perturbation composite control of a free-floating flexible dual-arm space robot

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Journal of Pharmaceutical Analysis 2008年第1期20卷 43-47,70页

作者：罗战武王从庆 College of Automation Engineering Nanjing University of Aeronautics and Astronautics

The Free-floating Flexible Dual-arm Space Robot is a highly nonlinear and coupled dynamics system. In this paper, the dynamic model is derived of a Free-floating Flexible Dual-arm Space Robot holding a rigid payload. Furthermore, according to the singular perturbation method, the system is separated into a slow subsystem representing rigid body motion of the robot and a fast subsystem representing the flexible link dynamics. For the slow subsystem, based on the second method of Lyapunov, using simple quantitative bounds on the model uncertainties, a robust tracking controller design is used during the trajectory tracking phase. The optimal control method is designed in the fast subsystem to guarantee the exponential stability. With the combination of the two above, the system can track the expected trajectory accurately, even though with uncertainty in model parameters, and its flexible vibration gets suppressed, too. Finally, some simulation tests have been conducted to verify the effectiveness of the proposed methods.

关键词： free-floating Flexible Dual-arm Space Robot singular perturbation robust tracking control vibration suppression

singular perturbation OF INITIAL VALUE PROBLEM FOR A NONLINEAR SECOND ORDER SYSTEMS

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Applied Mathematics and Mechanics(English Edition) 1993年第2期14卷 101-107页

作者：林宗池林苏榕 Department of Mathematics Fujian Normal University. Fuzhou Fujian Broadcasting TV University Fuzhou

In this paper, the singular perturbation of initial value problem for nonlinear second order vector differential equationsis discussed, where r>0 is an arbitrary constant, e>0 is a small parameter, x, f,a and Under suitable assumptions, by using the method of many-parameter expansion and the technique of diagonalization, the existence oj the solution of perturbation problem is proved and its uniformly valid asymptotic expansion of higher order is derived.

关键词： nonlinear system singular perturbation many-parameter expansion technique of diagonalization

Prediction of velocity distribution in straight open-channel flow with partial vegetation by singular perturbation method

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Applied Mathematics and Mechanics(English Edition) 2016年第10期37卷 1315-1324页

作者： Wenxin HUAI Suwen SONG Jie HAN Yuhong ZENG State Key Laboratory of Water Resources and Hydropower Engineering Science Wuhan University

A numerical analysis model based on two-dimensional shallow water differential equations is presented for straight open-channel flow with partial vegetation across the channel. Both the drag force acting on vegetation and the momentum exchange between the vegetation and non-vegetation zones are considered. The depth-averaged streamwise velocity is solved by the singular perturbation method, while the Reynolds stress is calculated based on the results of the streamwise velocity. Comparisons with the experimental data indicate that the accuracy of prediction is significantly improved by introducing a term for the secondary current in the model. A sensitivity analysis shows that a sound choice of the secondary current intensity coefficient is important for an accurate prediction of the depth-averaged streamwise velocity near the vegetation and non-vegetation interfaces, and the drag force coefficient is crucial for predictions in the vegetation zone.

关键词： depth-averaged velocity singular perturbation secondary flow