关于摄动分支问题的奇异摄动法

本文较全面地阐述了用奇异摄动法计算摄动分支问题(1.6)在y=0,λ=0,δ=0附近的解的一致渐近展式的一般数学原理和方法,并推广了牛顿多边形原理。最后,给出了两个计算实例。     

一类具有边界摄动的奇摄动问题

利用渐近理论,讨论了一类具有边界摄动的奇摄动问题.在适当的条件下,得出了这类问题解的存在性条件及其渐近解, 并将所得的结果应用于一类壁面波的传播问题.     

伴有边界摄动二阶非线性系统的奇摄动

讨论了伴有边界摄动的含积分算子的二阶非线性微分方程组边值问题的奇摄动.在适当的假设条件下,通过对角化技巧,证明了解的存在,并估计了余项.     

二阶奇摄动边值问题

本文应用上下解方法研究了边值问题εy"=f(t,y,ε),L(y(0),y'(0),ε)=0,R(y(1),y'(1),ε)=0(含一般的Robin问题)的解的存在性,唯一性和估计.     

自由边界摄动

关于自由边界,目前人们主要讨论一个障碍的问题,研究自由边界的确定和正规性。本文应用Lions的奇异摄动方法,讨论两个障碍的问题,研究自由边界之间的摄动关系和误差估计。     

具有边界摄动的非线性反应扩散方程奇摄动问题

研究了具有边界摄动的非线性反应扩散方程奇摄动问题．在适当的条件下,利用微分不等式理论,讨论了问题解的渐近性态．     

伴有边界摄动的向量高阶非线性边值问题的奇摄动

本文获得某类伴有边界摄动的向量高阶非线性微分方程边值问题解的存在性及其渐近估计式。     

奇摄动非线性边值问题

本文讨论了一类奇摄动非线性边值问题 .利用伸长变量和边界层校正法 ,得到了问题解的形式渐近展开式 .再用微分不等式理论 ,证明了解的一致有效性     

模糊推理的摄动性

在模糊推理过程中,推理前件的微小变化往往会引起推理结果的较大变化。针对这种情况,本文讨论基本模糊推理,多重模糊推理以及多重多维模糊推理的摄动性问题,并根据推理过程中复合算子和蕴涵算子的不同选取对各种形式的模糊推理的最大摄动参数进行评估。     

一类具有边界摄动的三阶非线性边值问题的奇摄动

关于三阶非线性奇摄动边值问题的研究,近年来,国内外学者做过一些研究。然而,关于这类问题解的唯一性问题,则仅仅在文献[4]、[5]中作过某些讨论。本文所要讨论的微分方程具有一种奇异特性,亦即fx″(t,x,x′,ε)≡0。而且当ε=0时三阶边值问题退化为一阶初值问题。所有这些特点,无疑将给对边值问     

A CLASS OF NONLINEAR SINGULARLY PERTURBED INITIAL BOUNDARY VALUE PROBLEMS FOR REACTION DIFFUSION EQUATIONS WITH BOUNDARY PERTURBATION

A class of nonlinear initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions and using the theory of differential inequalities the asymptotic solution of the initial boundary value problems is studied.     

THE NONLINEAR SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS WITH BOUNDARY PERTURBATION

The nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied.     

A Class of Nonlinear Singularly Perturbed Problems for Reaction Diffusion Equations with Boundary Perturbation

A class of nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary value problems is studied using the theory of differential inequalities.     

具有边界摄动的拟线性Robin问题

A class of quasilinear Robin problems with boundary perturbation are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the boundary value problem is studied.     

A Nonlinear Singularly Perturbed Problem for Reaction Diffusion Equations with Boundary Perturbation

A nonlinear singularly perturbed problems for reaction diffusion equation with boundary perturbation is considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary value problems of reaction diffusion equations is studied using the theory of differential inequalities.     

一类具有边界摄动的非线性泛函椭圆型方程奇摄动问题

研究了具有边界摄动的非线性泛函椭圆型方程奇摄动边值问题．在适当的条件下．利用伸长变量、微分不等式理论，讨论了问题解的渐近性态和原问题解的存在唯一性。     

反应扩散方程的奇摄动

§ 1　 IntroductionThe nonlinearsingularly perturbed problem is a very attractive subjectof study in theinternational academic circles[1 ] .During the past decade many approximate methods havebeen developed and refined,including the method of average,boundary layer method,matched asymptotic expansions,and multiple scales.Recently,many scholars,for example,Bohé[2 ] ,Butuzov and Smurov[3] ,O Malley[4] ,Butuzov,Nefedov and Schneider[5] ,Kelley[6]and so on did a great deal of work.Mo consider…     

A CLASS OF NONLINEAR NONLOCAL SINGULARLY PERTURBED PROBLEMS FOR ELLIPTIC EQUATION WITH BOUNDARY PERTURBATION

A class of nonlinear nonlocal singularly perturbed boundary value problems for elliptic equation with boundary perturbation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the stretched variable, the composing expansion method and the expanding theory of power series, the boundary layer is constructed, finally, using the theory of differential inequalities the asymptotic behavior of solution for the boundary value problems is studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed.     

高阶半线性椭圆型方程奇摄动广义Dirichlet边值问题

本文讨论了半线性椭圆型方程奇摄动广义边值问题,在适当的条件下研究了Dirichlet边值问题广义解的存在唯一性及其渐近性态。