BOUNDARY AND ANGULAR LAYER BEHAVIOR IN SINGULAR PERTURBED QUASILINEAR SYSTEMS

In this paper,using the method of differential inequalities,we study the existence ofsolutions and their asymptotic behavior,as ε→0~+,of Dirichlt problem for second orderquasilinear systems.Depending on whether the reduced solution u(t)has or does not havea continuous first-derivative in(a,b),we study two types of asymptotic behaviour,thusleading to the phenomena of boundary and angular layers.     

伴有边界摄动的一类四阶非线性微分方程解的估计

本文研究伴有边界摄动的一类四阶非线性微分方程边值问题 ε~2y~((4))=f(x, y, y′, y″, ε, μ), μ相似文献   

ASYMPTOTIC EXPERSSION OF THE SOLUTION OF GENERAL BOUNDARY VALUE PROBLEN FOR HIGHER ORDER ELLIPTIC EQUATION WITH PERTURBATION BOTH IN BOUNDARY AND IN OPERATOR

In this paper basing on (1) and (2),we study thesingular perturbation of general boundary value problemfor higher order elliptic equation with perturbationboth in the boundary and in the operator,so as to es-tablish the asymptotic expression involving two para-meters.Thus,the iterative process of finding theasymptotic solution is derived and the estimation ofthe remainder term is given out,we extend and improvethe previously published papers.     

SINGULAR PERTURBATION OF OPTIMAL CONTROL FOR SEMILINEAR INTEGRO-DIFFERENTIAL EQUATIONS

1 IlltroductionWe shall solve a problem Of optimal control consisting of the systemon the interval 0 5 t 5 1, with initial conditionsand the quadratic cost functionalwhich is to be minimized. Here the "T" denotes transposition; I = jot K(t, asx) fi are m-vectors; is gi are n-vectors, u is an r--vector, and the matrix R.is symmetric and positive definite, while the matrices Q and T are symmetricand positive semidefinite throughout 0 5 t S 1 for E > 0 small. fi, g2, 51 and6z are matrix functi…     

Dirichlet Problem of Higher Order Elliptic Equation with Perturbation both in Differential Operator and in Boundary

This paper is the continuation of article[7].It gives further results about the asymptoticexpression for the solution of higher order elliptic equation in the case of boundary perturbationcombined with operator perturbation.When unperturbed problem Ao is not on the spectrum,theasymptotic expression for the solution of perturbation problem Aεmay be expanded with respectto the small parameterε.While Ao is on the spectrum,the asymptotic expression of the solutioncontains negative powers of the small parameterε.The approximation of arbitrary order to thesolution is considered and the recursive formula for the general term and the estimation of remain-der term are given.     

Asymptotic solution of a singularly perturbed nonlinear state regulator problem

I.1utroductlouWeconsidcrthenonlinearstateregulatorproblemsconsistingofthesystemontheinterval0't相似文献   

Boundary and angular layer behavior in singular perturbed quasilinear systems

In this paper, using the method of differential inequalities, we study the existence of solutions and their asymptotic behavior, as 0⁺, of Dirichlt problem for second order quasilinear systems. Depending on whether the reduced solutionu(t) has or does not have a continuous first-derivative in (a, b), we study two types of asymptotic behaviour, thus leading to the phenomena of boundary and angular layers.     

再论方程带两个小参数的高阶椭圆型方程一般边值问题的奇摄动

本文用“两变量展开程序”[12]的方法重新研究方程带两个小参数的高阶椭圆型方程一般边值问题解的渐近式的构造,这个问题的边值条件比文[l]更一般.我们给出了渐近解的表达式和有关的余项估计.     

边界和算子双摄动的高阶椭圆型方程一般边值问题解的渐近式

本文在文[1]和[2]的基础上研究边界和算子双摄动的高阶椭圆型方程一般边值问题的奇摄动,建立含两参数的渐近解表达式,导出求渐近解的迭代过程,给出余项估计,改进和拓广了前文的工作.     

Singular perturbation of boundary value problem of systems for quasilinear ordinary differential equations

In this paper,we study the singular perturbation of boundary value problem of systemsfor quasilinear ordinary differential equations:x′=f(t,x,y,ε),εy″=g(t,x,y,ε)y′ h(t,x,y,ε),x(0,ε)=A(ε),y(0,ε)=Bε,y(1,ε)=C(ε)where xf.y,h,A,B and C belong to R″and a is a diagonal matrix.Under the appropriateassumptions,using the technique of diagonalization and the theory of differentialinequalities we obtain the existence of solution and its componentwise uniformly validasymptotic estimation.