SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR SEMI-LINEAR RETARDED DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

IntroductionInthispaper,westudiedakindofboundaryvalueproblems (BVPs)forsemi_linearretardeddifferentialequationwithnonlinearboundarycondition :　　　　εx″(t) =f(t,x(t) ,x(t-ε) ,ε) ,　　t∈(0 ,1 ) ,(1 )　　　　x(t) =φ(t,ε) ,　t∈[-ε0 ,0 ] ,h(x(1 ) ,x′(1 ) ,ε) =A(ε) ,(2 )whereε>0isasmallparameterandε0 isasufficientlysmallpositiveconstant.ThereweremanyresultsofstudyingonsingularlyperturbedboundaryvalueproblemforretardeddifferentialequationinRefs.[1～5] .Butthosestudiespossessedanesse…     

THE NUMERICAL SOLUTION OF A SINGULARLY PERTURBED PROBLEM FOR SEMILINEAR PARABOLIC DIFFERENTIAL EQUATION

The numerical solution of a singularly perturbed problem for the semilinear parabolicdifferential equation with parabolic boundary layers is discussed.A nonlinear two-leveldifference scheme is constructed on the special non-uniform grids.The uniform convergenceof this scheme is proved and some numerical examples are given.     

NUMERICAL SOLUTION OF THE SINGULARLY PERTURBED PROBLEM WITH NONLOCAL BOUNDARY CONDITION

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｉｓｐａｐｅｒｉｓｃｏｎｃｅｒｎｅｄｗｉｔｈｔｈｅｎｕｍｅｒｉｃａｌｓｏｌｕｔｉｏｎ ,ｂｙｆｉｎｉｔｅｄｉｆｆｅｒｅｎｃｅｍｅｔｈｏｄ ,ｏｆｔｈｅｆｏｌｌｏｗｉｎｇｓｉｎｇｕｌａｒｌｙｐｅｒｔｕｒｂｅｄｎｏｎｌｏｃａｌｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍ :Ｌｕ≡-εｕ″ +ａ(ｘ)ｕ=ｆ(ｘ)　　 ( 0 <ｘ<ｌ) ,( 1 )Ｌ0 ｕ≡-εｕ′( 0 ) +γｕ( 0 ) =μ0 , ( 2 )Ｌ1ｕ≡ｕ(ｌ) -δｕ(ｄ) =μｌ　　 ( 0 <ｄ<ｌ) ,( 3 )ｗｈｅｒｅεｉｓａｓｍａｌｌｐｏｓｉｔｉｖｅｐａｒａｍｅｔｅｒ,…     

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

A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, first, the outer solution of the original problem was obtained. Secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer was constructed. Finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems was studied, and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation were discussed.     

SINGULAR PERTURBATION OF INITIAL BOUNDARY VALUE FROBLEMS OF REACTION DIFFUSlON EQUATION WITH DELAY

ＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＯＦＩＮＩＴＩＡＬＢＯＵＮＤＡＲＹＶＡＬＵＥＦＲＯＢＬＥＭＳＯＦＲＥＡＣＴＩＯＮＤＩＦＦＵＳｌＯＮＥＱＵＡＴＩＯＮＷＩＴＨＤＥＬＡＹＺｈａｎｇＸｉａｎｇ（张祥）（ＡｎｈｕｉＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）Ｗｕ...     

APPLICATION OF THE DUAL RECIPROCITY BOUNDARY ELEMENT METHOD TO SOLUTION OF NONLINEAR DIFFERENTIAL EQUATION

In this paper the dual reciprocity boundary element method is employed to solve nonlinear differential equation ∇² u+u+ɛu ³ =b. Results obtained in an example have a good agreement with those by FEM and show the applicability and simplicity of dual reciprocity method(DRM)in solving nonlinear differential equations.     

A MIXED ELECTRIC BOUNDARY VALUE PROBLEM FOR AN ANTI－PLANE PIEZOELECTRIC CRACK

The analytical continuation method is adopted to solve a mixed electric boundary value problem for a piezoelectric medium under anti-plane deformation. The crack face is partly conductive and partly impermeable. The results show that the stress intensity factor is identical with the mode III stress intensity factor independent of the conducting length. But the electric field and the electric displacement are dependent on the electric boundary conditions on the crack faces and are singular not only at the crack tips but also at the junctures between the impermeable part and conducting portions.     

PHRAGMEN－LINDELOF ALTERNATIVE RESULTS FOR THE INITIAL BOUNDARY PROBLEM OF STOKES EQUATION

ＰＨＲＡＧＭＥＮ－ＬＩＮＤＥＬＯＦＡＬＴＥＲＮＡＴＩＶＥＲＥＳＵＬＴＳＦＯＲＴＨＥＩＮＩＴＩＡＬＢＯＵＮＤＡＲＹＰＲＯＢＬＥＭＯＦＳＴＯＫＥＳＥＱＵＡＴＩＯＮＣａｉＣｈｏｎｇｘｉ（蔡崇喜）ＬｉｎＣｈａｎｇｈａｏ（林长好）（ＺｈｏｎｇｓｈａｎＵｎｉｖｅ...     

EXISTENCE OF SOLUTIONS FOR HIGHER ORDER MULTI-POINT BOUNDARY VALUE PROBLEM AT RESONANCE

Using the theory of coincidence degree, a class of higher order multi-point boundary value problem for ordinary differential equations are studied. Under the boundary conditions satisfying the resonance case, some new existence results are obtained by supposing some conditions to the nonlinear term and applying a priori estimates.     

含孔von Karman板中非线性波散射与边值问题

基于ｖｏｎ Ｋａｒｍａｎ板大挠度弯曲理论,利用小参数摄动法,分析研究了含孔ｖｏｎＫａｒｍａｎ板的非线性波散射与动应力集中问题,其中一类可看成是薄板弯曲波动问题的控制方程。当有单频波入射时,由于弯曲应力与膜应力状态的非线性耦合,孔洞会产生高次谐波散射现象。建立了求解本问题的边界积分方程法,利用积分方程法交替求求这两类问题,最终可获得问题的近似分析解。     

A NEW EFFICIENT METHOD TO BOUNDARY VALUE PROBLEM FOR BALLISTIC ROCKET GUIDANCE

IntroductionThe problem of motion control for the mass center of ballistic rocket pertained typicallyto the boundary value problem for two points with the non-linear and multi-variables,namely,given the initial states of rocket,in order to satisfy the res…     

GLOBAL SOLUTION OF THE INVERSE PROBLEM FOR ACLASS OF NONLINEAR EVOLUTION EQUATIONSOF DISPERSIVE TYPE

ＩｎｔｒｏｄｕｃｔｉｏｎＩｔｉｓｗｅｌｌ＿ｋｎｏｗｎｔｈａｔｐｓｅｕｄｏ＿ｐａｒａｂｏｌｉｃｅｑｕａｔｉｏｎｗｉｔｈｐｒｉｎｃｉｐａｌｐａｒｔｕｔ -ｕｘｘｔｈａｓｂｅｅｎｓｔｕｄｙｉｎｇｒｅｃｅｎｔｌｙ ,ｂｅｃａｕｓｅｔｈｅｒｅｅｘｉｓｔｓｗｉｄｅｐｈｙｓｉｃａｌｂａｃｋｇｒｏｕｎｄｆｏｒｔｈｉｓｃｌａｓｓｏｆｅｑｕａｔｉｏｎｓ.[1 ]ｓｔｕｄｉｅｄｔｈｅｍｕｌｔｉ＿ｄｉｍｅｎｓｉｏｎｉｎｖｅｒｓｅｐｒｏｂｌｅｍｆｏｒｔｈｅｆｏｌｌｏｗｉｎｇｃｌａｓｓｏｆｎｏｎｌｉｎｅａｒｅｖｏｌｕｔｉｏｎｅｑｕ…     

SINGULAR PERTURBATIONS FOR A CLASS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER NONLINEAR DIFFERENTIAL EQUATIONS

ＳＩＮＧＵＬＡＲ　ＰＥＲＴＵＲＢＡＴＩＯＮＳ　ＦＯＲ　Ａ　ＣＬＡＳＳ　ＯＦ　ＢＯＵＮＤＡＲＹ　ＶＡＬＵＥ　ＰＲＯＢＬＥＭＳ　ＯＦ　ＨＩＧＨＥＲ　ＯＲＤＥＲ　ＮＯＮＬＩＮＥＡＲ　ＤＩＦＦＥＲＥＮＴＩＡＬ　ＥＱＵＡＴＩＯＮＳＳｈｉＹｕａｎｉｎｇ（史玉明）...     

ASYMPTOTIC NON-STABILITY AND BLOW-UP AT BOUNDARY FOR SOLUTIONS OF A FILTRATION EQUATION

For a class of nonlinear filtration equation with nonlinear second-third boundary value condition, it is shown that a priori boundary of the solution can be estimated and controlled by initial data and integral on the boundary of the region. The priori estimate of the solutions was established by iterative method. By using this estimate the solutions may blow-up on the boundary of the region and thus it may have asymptotic non-stability.     

处理一种非线性问题迭代法的计算机方法

本文依非线性问题的积分方程组,按迭代法得出一般迭代表达式.由此,任意次迭代解的所有待定系数可用计算机计算,使研究复杂的非路性问题成为可能.     

边值问题中与分离变量法等价的级数解法

用带奇性分离的Ｆｏｕｒｉｅｒ级数解平面边值问题，改进了不能满足全部边界条件的一般级数解法，得到收敛较好的解析算法。文中证明了级数解法与分离变量法的等价性，由此将分离变量解所得的非线性特征方程转化为多项式方程，为近似算法与渐近分析提供了依据。     

A SPECIAL METHOD OF FOURIER SERIES WHICH IS EQUAL TO THE METHOD OF SEPARATION OF VARIABLES ON BOUNDARY VALUE PROBLEM

By the separation of singularity, a special Fourier series solution of the boundary valueproblem for plane is obtained, which can satisfy all boundary conditions and converges rapidly. It isproved that the solution is equal to the result of separation of variables. As a result, the non-linearcharacteristic equations resulting from the method of separation of variables are transformed into poly-nomial equations that can provide a foundation for approximate computation and asymptotic analysis.     

压电介质二维边界积分方程中的基本解

由于压电介质的变形－电场耦合效应及压电响应的各向异性，使解析求解压电介质问题的工作变量十分复杂，若采用边界元数值方法求解，必须具备积分方程中的基本解，本文根据电磁场方程及连续介质力学的耦合性质论层出了二维无限域中分别在单位力及单位电荷载作用下的位移场，电势场、应力场和电位移场的解，从而确立了边界积分方程中所必需的八个基本解。