A Perturbation Solution for a Two-dimensional Annular Electrochemical Machining Problem

Present address: Deparment of Applied Mathematics, University of Western Ontario, London, Canada. A two-dimensional electrochemical machining problem which consistsof an almost circular anode placed inside a circular cathodeis solved using a perturbation procedure. The smoothing of roughmetal parts is studied by solving the resulting perturbationequations numerically.     

On the Approximate Solution of a Diffusion Problem by Galerkin Methods

Discrete-time Galerkin methods are considered for the approximatesolution of a parabolic initial boundary value problem whicharises, for example, in problems involving the diffusion ofa solute into a solid from a stirred solution of fixed volume.Optimal error estimates in the L² and H¹ norms are derived forthe Crank-Nicolson Galerkin method. For the one space variablecase optimal L estimates are also obtained. Results of numericalexperiments are presented and comparisons with finite differenceapproximations are made.     

二维实用下料问题的数学模型及较优解

二维下料问题是2004年首届全国部分高校研究生数学建模竞赛B题.建立了二维下料问题的数学模型,找到了用料451块,下料方式数为37的较优解,并证明了此问题总用料的下界是449块.     

A Global Solution to a Two-dimensional Riemann Problem Involving Shocks as Free Boundaries

We present a global solution to a Riemann problem for the pressure gradient system of equations.The Riemann problem has initially two shock waves and two contact discontinuities. The angle between the two shock waves is set initially to be close to 180 degrees. The solution has a shock wave that is usually regarded as a free boundary in the self-similar variable plane. Our main contribution in methodology is handling the tangential oblique derivative boundary values.     

The Solution of a Singularly Perturbed Convection–Diffusion Problem by an Iterative Domain Decomposition Method

This paper deals with an iterative algorithm for domain decomposition applied to the solution of a singularly perturbed convection–diffusion problem. Convergence properties of the algorithm are established. Numerical results are presented.     

A Moving Boundary Problem Arising from the Diffusion of Oxygen in Absorbing Tissue

Approximate analytical and numerical solutions of a partialdifferential equation are obtained which describe the diffusionof oxygen in an absorbing medium. Essential mathematical difficultiesare associated with the presence of a moving boundary whichmarks the furthest penetration of oxygen into the medium andalso with the need to allow for an initial distribution of oxygenthrough the medium.     

半线性奇摄动反应扩散方程初边值问题解的渐近性(英文)

本文运用边界层以及角点层函数法构造了一类半线性奇摄动反应扩散方程初边值问题解的渐近展开式 ,并用微分不等式方法证明了该展式达到任一精度的一致有效性     

一类扩散型变分方程问题

本文讨论了扩散型方程的某些分析性质,得到了一些较为深刻的结论,并应用这些结论证明了一类扩散型变分方程解的存在性。同时,还指出这类变分方程在随机控制的研究中有着重要的理论意义。     

The Cauchy Problem for a Nonlinear Diffusion Equation with Absorption and Convection

In this paper we construct the large-time solution of the equation which models the effectof nonlinear absorption on thin film flow of a viscous fluidon a sloping bed. For initial data with finite support we showhow the asymptotic structure of the Cauchy problem depends onthe absorption index . An important addition motivation forthe study is to provide a basis for extending the results tothe more general equation which has applications in plasma physics.     

Singular Perturbation in a Nonlocal Diffusion Problem

We study a singular perturbation problem for a nonlocal evolution operator. The problem appears in the analysis of the propagation of flames in the high activation energy limit, when admitting nonlocal effects.

We obtain uniform estimates and we show that, under suitable assumptions, limits are solutions to a free boundary problem in a viscosity sense and in a pointwise sense at regular free boundary points.

We study the nonlocal problem both for a single equation and for a system of two equations.

Some of the results obtained are new even when the operator under consideration is the heat operator.     

The Solution of a Railway Locomotive Scheduling Problem

A method is described for finding a minimum cost set of schedules for railway locomotives to work a given set of trains. The times at which the trains start may be fixed or variable. A heuristic method, based on a linear programming model, is described. This gives good integer solutions to the problem.     

Fourier Problem for a Coupled Diffusion System with Functionals

We investigate the well-posedness of a problem for a system of functional differential equations of different types without initial conditions. Each equation consists of two parts one of which has the same structure as a parabolic equation or an ordinary differential equation with parameters, while the other contains functionals defined on a space of functions continuous in space variables.     

The Numerical Solution of a Minimization Problem Associated with a Free Surface Flow

The solution of the differential equation governing the seepageof fluid through a porous dam can be shown to be equivalentto the minimization of a quadratic functional over a fixed rectangularregion. The latter problem is solved using the method of finiteelements, and the results compared with earlier computations.An analysis of the singularity at the separation point is usedto find the position of the separation point.     

The Numerical Solution of a Variational Problem in Automatic Control

In this paper we examine the numerical solution of a two-pointboundary value problem whose boundary condition depends on thevalue of the solution at interior points.     

一类具有转向点问题的n阶近似解

用Langer变换和Olver变换求得一类具有转向点问题的n阶近似解:y(x)=v(x)ψ(x),其中ψ=λ12-14×(x2-1)14,2332=-λx∫11-τ2dτ,v(z)=A(z,λ)ξ(λ23z)+B(z,λ)'ζ(λ23z).并探讨了其特征值问题,得到λn=4n+1112,n=0,1,2….由此给出了该类问题的解的一般性结论.     

一类Stefan问题的渐近解

本文讨论了一类具有一般初值条件的Stefan问题.把研讨论板分成三部份,每一部份选用不同的时间尺度,然后用PLK方法或类多重尺度法求得每一部份的渐近解.最后,就此解进行了讨论并得出相应的结论.     

Solution of a Contact Elasticity Problem with a Rigid Inclusion

Computational Mathematics and Mathematical Physics - An equilibrium problem for an elastic body containing a rigid inclusion is solved. There is a delamination crack on a portion of the interface...