THE UNIQUENESS AND EXISTENCE OF SOLUTION OF THE CHABACTERISTIC PROBLEM ON THE GENERALIZED KdV EQUATION

ＴＨＥＵＮＩＱＵＥＮＥＳＳＡＮＤＥＸＩＳＴＥＮＣＥＯＦＳＯＬＵＴＩＯＮＯＦＴＨＥＣＨＡＢＡＣＴＥＲＩＳＴＩＣＰＲＯＢＬＥＭＯＮＴＨＥＧＥＮＥＲＡＬＩＺＥＤＫｄＶＥＱＵＡＴＩＯＮＬｉＷｅｎ－ｓｈｅｎ（李文深）（ＮｏｒｔｈｅａｓｔＦｏｒｅｓｔｒｙＵｎｉｖ...     

Numerical solution of nonlinear ordinary differential equation for a turning point problem

By using the method in[3],several useful estimations of the derivatives of the solutionof the boundary value problem for a nonlinear ordinary differential equation with a turningpoint are obtained.With the help of the technique in[4],the uniform convergence on thesmall parameterεfor a difference scheme is proved.At the end of this paper,a numericalexample is given.The numerical result coincides with theoretical analysis.     

On the uniqueness of boundary integral equation for the exterior Helmholtz problem

From the point of view of energy analysis,the cause that the uniqueness of theboundary integral equation induced from the exterior Helmholtz problem does not hold isinvestigated in this paper.It is proved that the Sommerfeld’s condition at the infinity ischanged so that it is suitable not only for the radiative wave but also for the absorptive wavewhen we use the boundary integral equation to describe the exterior Helmholtz problem.Therefore,the total energy of the system is conservative.The mathematical dealings toguarantee the uniqueness are discussed based upon this explanation     

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.     

ON THE EXISTENCE AND STABILITY OF SOLUTION FOR SEMI－HOMOGENEOUS BOUNDARY VALUE PROBLEM

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＳＴＡＢＩＬＩＴＹＯＦＳＯＬＵＴＩＯＮＦＯＲＳＥＭＩ－ＨＯＭＯＧＥＮＥＯＵＳＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＤｏｎｇＱｉｎｘｉ（董勤喜）;ＨｕａｎｇＸｉａｎｋａｉ（黄先开）（ＲｅｃｅｉｖｅｄＪｕｌｙ．４．１９...     

Existence of periodic traveling wave solutions for a class of generalized BBM equation

In this paper, a new kind of generalized BBM equation is introduced and discussed. Some existence theorems of periodic traveling wave solutions for this kind generalized BBM equation are given.     

The existence of solution of a class of two-order quasilinear boundary value problem

Ref. [1] discussed the existence of positive solutions of quasilinear two-point boundary problems: but it restricts O相似文献   

One approximate solution of the Nekrasov problem

An approximate solution ω = A[ω, μ] of the nonlinear integral Nekrasov equation is obtained by successive replacement of the kernel of the integral operator by a close one. The solution is sought not directly at the bifurcation point μ₁ = 3 of the linearized equation ω = μL[ω] but at the point μ = 1 at which operator A[ω, μ], remaining nonlinear in ω, is linear in μ. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 50–56, November–December, 2007.     

THE EXISTENCE OF PERIODIC SOLUTION OF THE FOURTH ORDINARY NONLINEAR DIFFERENTIAL EQUATION CAUSED BY FLOW－IN

ＴＨＥＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＯＦＴＨＥＦＯＵＲＴＨＯＲＤＩＮＡＲＹＮＯＮＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＣＡＵＳＥＤＢＹＦＬＯＷ－ＩＮＤＵＣＥＤＶＩＢＲＡＴＩＯＮＧｕＱｉｎｇ－ｆａｎｇ（顾清芳）Ｔａ...     

Problem of periodic solutions for neutral functional differential equation

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＣ(ｋ- 1)2π =ｈ(ｔ) ｜ｈ :Ｒ →Ｒｉｓ (ｋ -1 )＿ｔｈｏｒｄｅｒｃｏｎｔｉｎｕｏｕｓｄｉｆｆｅｒｅｎｔｉａｂｌｅａｎｄｈ(ｔ+ 2π) ≡ｈ(ｔ) ,　　Ｃ2π =ｈ(ｔ) ｜ｈ :Ｒ →Ｒｉｓｃｏｎｔｉｎｕｏｕｓａｎｄｈ(ｔ+ 2π) ≡ｈ(ｔ) ,　　‖ｈ(ｔ)‖ =ｓｕｐｔ∈ [0 ,2π] ｜ｈ(ｔ) ｜ ,　　‖ｈ(ｔ)‖Ｐｋ- 1 =ｍａｘ‖ｈ(ｔ)‖ ,‖ｈ′(ｔ)‖ ,… ,‖ｈ(ｋ- 1) (ｔ)‖ ,　　ｘ(ｍ) (ｔ+ ·) (θ) =ｘ(ｍ) (ｔ+θ)　　θ∈Ｒ (ｍ =0 ,1 ,2 ,… ,ｋ-1 ) .Ｃｌｅａｒｌｙ ,ｘ(ｍ) (ｔ + ·) ∈Ｃ2π, …     

Numerical solution of multiple hole problem by using boundary integral equation

This paper studies a numerical solution of multiple hole problem by using a boundary integral equation. The studied problem can be considered as a supposition of many single hole problems. After considering the interaction among holes, an algebraic equation is formulated, which is then solved by using an iteration technique. The hoop stress around holes can be finally determined. One numerical example is provided to check its accuracy.     

The numerical solution of a singularly perturbed problem for quasilinear parabolic differential equation

We consider the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation, and construct a linear three-level finite difference scheme on a nonuniform grid. The uniform convergence in the sense of discrete L~2 norm is proved and numerical examples are presented.     

The existence and uniqueness of weak solution of the flow between two concentric rotating spheres

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ,ｗｅｓｔｕｄｙｔｈｅｕｎｓｔｅａｄｙａｘｉｓｙｍｍｅｔｒｉｃｉｎｃｏｍｐｒｅｓｓｉｂｌｅｆｌｏｗｂｅｔｗｅｅｎｔｗｏｃｏｎｃｅｎｔｒｉｃｓｐｈｅｒｅｓ．Ｔｈｉｓｆｌｏｗｉｓｃａｌｌｅｄａｓｓｐｈｅｒｉｃ...     

Darboux transformation of generalized coupled KdV soliton equation and its odd-soliton solutions

Based on the resulting Lax pairs of the generalized coupled KdV soliton equation, a new Darboux transformation with multi-parameters for the generalized coupled KdV soliton equation is derived with the help of a gauge transformation of the spectral problem. By using Darboux transformation, the generalized odd-soliton solutions of the generalized coupled KdV soliton equation are given and presented in determinant form. As an application, the first two cases are given.     

SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEM FOR A KIND OF VOLTERRA TYPE FUNCTIONAL DIFFERENTIAL EQUATION

IntroductionThereweresomeresultsofstudyingonboundaryvalueproblemsforfunctionaldifferentialequation[1～6 ]byemployingthetoplolgicaldegreetheoryandsomefixedpointprinciplesinrecentyears.Buttheworktostudyboundaryvalueproblemsfordelaydifferentialequationwithsmallparameterbymeansofthetheoryofsingularperturbationrarelyappeared[7～11].Thereasonforitisthattheworktoconstructtheuppersolutionandlowersolutionforthecaseofdifferentialequationwithdelayisdifficult.Theauthorhasstudiedakindofboundaryvalueproblem…     

广义KdV方程Fourier谱逼近的最优误差估计

A Fourier spectral method for the generalized Korteweg-de Vries equation with periodic boundary conditions is analyzed, and a corresponding optimal error estimate in L^2-norm is obtained. It improves the result presented by Maday and Quarteroni. A modified Fourier pseudospectral method is also presented, with the same convergence properties as the Fourier spectral method.     

A COMPLETE EXPRESSION OF THE ASYMPTOTIC SOLUTION OF DIFFERENTIAL EQUATION WITH A∩-TH ORDER TURNING POINT

A second order linear ordinary differential equation has been studied, and the complete expresson, of the formal uniformly valid asymptotic solutions to the equation near turning point is obtained by using extended Airy function.     

On the formal solution of initial value problem of Navier-Stokes equation

Ｉｎｒｅｆｅｒｅｎｃｅ [1 ] ,ｗｅｄｉｓｃｕｓｓｅｄｔｈｅｉｎｓｔａｂｉｌｉｔｙｏｆＮａｖｉｅｒ＿ＳｔｏｋｅｓｅｑｕａｔｉｏｎｏｎＲ3×Ｒ ,ａｎｄ ,ｉｎｔｈｅｉｌｌｕｓｔｒａｔｉｏｎｏｆｉｔ,ｗｅｐｒｅｓｅｎｔｅｄｓｏｍｅｅｘａｍｐｌｅｓｉｎｔｈｅｆｏｒｍｏｆｅｘａｃｔｓｏｌｕｔｉｏｎ .Ｔｈｅｂａｓｉｓｏｆｔｈｅｃｏｎｓｔｒｕｃｔｉｏｎｏｆｔｈｅｍｉｓｔｈｅ“ｅｑｕａｔｉｏｎｓｅｃｏｎｄａｉｒｅ”ｏｆｔｈｅｅｑｕａｔｉｏｎ .Ｉｎｆａｃｔ,ｔｈｅｓｅｅｘａｃｔｓｏｌｕｔｉｏｎｓａｒｅｓｏｍｅｌｉｍｉｔ…     

Instability of solution for the fourth order linear differential equation with varied coefficient

In this paper,we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient,at least one of the characteristic roots of which has positive real part,by means of Liapunov’s second method.     

Positive solutions to (n-1,1) m-point boundary value problems with dependence on the first order derivative

Using the extension of Krasnoselskii's fixed point theorem in a cone, we prove the existence of at least one positive solution to the nonlinear nth order m-point boundary value problem with dependence on the first order derivative. The associated Green's function for the nth order m-point boundary value problem is given, and growth conditions are imposed on the nonlinear term f which ensures the existence of at least one positive solution. A simple example is presented to illustrate applications of the obtained results.