关于热传导自由边界问题的探讨

对钢锭冷凝过程的研究,归结为求解组合介质热传导自由边界问题.本文就未凝固的钢水中热传导问题进行了探讨.即讨论下面的定解问题:     

用Fourier方法解半线性抛物型方程双移动边界问题

文[1]就金属板烧蚀中提出的问题,给出了热导方程单个移动边界问题的Fourier型级数求解法。文[2]研究了热导方程双移动边界问题。还有些人研究了抛物型方程移动边界问题情况。但是迄今这一类问题的研究工作集中于线性的情况,对非线性的情况讨论甚少,其它移动边界问题也是如此(参见[3]、[4])。本文是在[1]、[2]的基础上,讨论如下的一类半线性抛物型方程双移动边界的定解问题:     

一类抛物型方程移动边界问题的付氏解

<正> 众所周知,移动边界问题在物理和工程上有广泛的应用。文[1]就金属板烧蚀中提出的问题,提供了热导方程移动边界问题的Fourier型级数求解法,应用价值较大。本文是在[1]的基础上讨论一类更广泛的问题。     

无限域上一维热传导方程的Gauss-Laguerre数值解

针对无限域上一维热传导方程的解析解为反常积分形式,直接计算往往比较困难.首先采用Fourier变换给出问题解析解,其次结合解析解的形式和无限域上Gauss型数值积分法精度高的优点,将半无限域上的一维热传导方程问题利用Gauss-Laguerre数值积分计算数值解,对无限域上的一维热传导方程的解析解转化为半无限域上的形式后用Gauss-Laguerre数值积分计算.实验结果表明,本文给出的数值解方法具有很高的精度.     

一类非线性反向热传导问题的Fourier正则化方法

考虑了非线性抛物方程反向热传导问题,这类问题是不适定的,即问题的解不连续依赖于测量数据.利用Fourier截断正则化方法恢复其不适定性,得到问题的一个正则近似解,并且给出正则解和精确解之间具有Hlder型的误差估计.     

求解一般抛物方程侧边值问题的具H■lder连续性的Fourier正则化方法

逆热传导问题是严重不适定问题,它的解如果存在,其解将不连续依赖于定解数据,使得数值计算和理论分析都非常困难.但目前关于逆热传导问题的已有文献大都主要集中于讨论由标准热传导方程所描述的问题.该文给出了一种适用于由一般一维抛物方程所描述的逆热传导问题且具有Ho。lder连续性的Fourier正则化新方法.     

一个非标准逆热传导问题的具有对数稳定性的Fourier正则化方法

逆热传导问题是严重不适定问题,即问题的解(如果存在)将不连续依赖于测量数据,使其数值计算非常困难.但最近20 年来人们主要关注标准的逆热传导问题而对非标准情形研究较少.本文给出了一个非标准逆热传导问题的具有对数稳定性的Fourier正则化方法,恢复了解对数据的连续依赖性.     

求热导方程移动边界问题近似解的一个方法

众所周知,热导方程的移动边界问题可以用来描述如金属板烧蚀等一类物理现象,科学技术的实际应用要求热导方程移动边界问题近似求解,但迄今为止还未能找到令人满 意的求解方法.本文提供一个类似 Fourier 级数的近似求解法及有关的实际应用.     

一类非饱和流动的Fourier级数解(英)

本文研究带有抽取的非饱和流动中出现的一个非线性边值问题．利用互惠变换及HopfCole变换将问题化为一个移动边界问题，进而获得了Fourier级数解．     

求解一般抛物方程侧边值问题的Fourier正则化方法

逆热传导问题是严重不适定问题,它的解如果存在,其解将不连续依赖于定解数据,使得数值计算和理论分析都非常困难。但目前关于逆热传导问题的已有文 献大都主要集中于讨论由标准热传导方程所描述的问题。该文给出了一种适用于由一般一维抛物方程所描述的逆热传导问题且具有Holder连续性的Fourier正则化新方法。     

Finite difference reaction diffusion equations with nonlinear boundary conditions

This article is concerned with numerical solutions of finite difference systems of reaction diffusion equations with nonlinear internal and boundary reaction functions. The nonlinear reaction functions are of general form and the finite difference systems are for both time-dependent and steady-state problems. For each problem a unified system of nonlinear equations is treated by the method of upper and lower solutions and its associated monotone iterations. This method leads to a monotone iterative scheme for the computation of numerical solutions as well as an existence-comparison theorem for the corresponding finite difference system. Special attention is given to the dynamical property of the time-dependent solution in relation to the steady-state solutions. Application is given to a heat-conduction problem where a nonlinear radiation boundary condition obeying the Boltzmann law of cooling is considered. This application demonstrates a bifurcation property of two steady-state solutions, and determines the dynamic behavior of the time-dependent solution. Numerical results for the heat-conduction problem, including a test problem with known analytical solution, are presented to illustrate the various theoretical conclusions. © 1995 John Wiley & Sons, Inc.     

On the spectrum of a multipoint boundary value problem for a fourth-order equation

We study the spectral properties of a multipoint boundary value problem for a fourth-order equation that describes small deformations of a chain of rigidly connected rods with elastic supports. We study the dependence of the spectrum of the boundary value problem on the rigidity coefficients of the supports. We show that the spectrum of the boundary value problem splits into two parts, one of which is movable under changes of the rigidity coefficients and the other remains fixed. As the rigidity coefficients grow, the eigenvalues corresponding to the movable part of the spectrum grow as well; moreover, the double degeneration of some eigenvalues is possible.     

The thermal wake of a streamlined body

The stationary problem of the thermal wake behind a body around which there is a flow of a viscous incompressible fluid is considered within the framework of the full heat-conduction equation. It is assumed that the solution of the corresponding hydrodynamic problem is known. In the case of the hydrodynamic problem, theorems of existence [1,2] and uniqueness [1] have been proved and the leading term of the expansion [1, 3] at an infinitely remote point has been obtained together with estimates of the remaining terms [1, 4]. Work mainly carried out within the framework of the boundary layer approximation [5] is concerned with the solution of the thermal problem.     

半导体问题的向后差分配置法及误差分析

Collocation method is put forward to solve the semiconductor problem with heat-conduction, whose mathematical model is described by an initial and boundary problem for a nonlinear partial differential equation system. One elliptic equation is for the electric potential, and three parabolic equations are for the electron concentration, hole concentration and heat-conduction. Using the prior estimate and technique of differential equations, we obtained almost optimal error estimates in L2.     

三维热传导型半导体问题的特征混合元方法和分析

本文研究三维热传导型半导体态问题的特征混合元方法及其理论分析,其数学模型是一类非线性偏微分方程的初边值问题,对电子位势方程提出混合元逼近,对电子,空穴浓度方程笔挺表限元逼近;对热传导方程采用对时间向后差分的Ｇａｌｅｒｋｉｎ逼近,应用微分方程先验估计理论和技巧得到了最优阶Ｌ＾２误差估计。     

ALTERNATING-DIRECTION MULTISTEP PRECONDITIONED ITERATIVE METHODS FOR SEMICONDUCTOR PROBLEM WITH HEAT-CONDUCTION

The model of transient behavior of semiconductor with heat-conduction is an initial and boundary problem. Alternating-direction multistep preconditioned iterative methods and theory analyses are given in this paper. Electric potential equation is approximated by mixed finite element method, concentration and heat-conduction equations are approximated by Galerkin alternating-direction multistep methods. Error estimates of optimal order in L2 are demonstrated.     

热传导方程的小波解法

本文利用微分算子的小波表示，讨论一维热传导方程初值问题的Daubechies小波解，给出此问题的显式离散格式。由于小波在时间和频率上的局部性，此方法特别适用于有奇异解的热传导方程，逼近精度高，而且没有发生解的振荡现象。     

A numeric-analytic method of solving a nonlinear problem of heat conduction for a right prism

Using the example of solving a nonlinear steady-state heat-conduction problem we show the efficiency of the simultaneous application of the loading, splitting, iteration, and projection-grid methods, as well as the use of a fundamental solution and the method of boundary elements for determining the temperature fields in bodies of complicated geometrical shape.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 31, 1990, pp. 95–99.     

THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR THE NONLINEAR HEAT-CONDUCTION EQUATION AND ITS APPLICATION

1 IntroductionIn the heat-conduction equationp is the density,c is the specific heat,k is the thermal conductivityLet u = w -- wco be therelative temperature, where woo is the environmental temperature. In many cases, the thermalconductivity k is dependent of the temperature,forrexample, the heat-conduction of electron iuthe plasma body and the radiation heat-conduction in the high temperature,k(u) = uoum--' (m > 1).Assume that p, c are constants, then the equation (1.1) can be written asWe c…     

Solvability of problems with degeneration: Imbibition of fluid in a porous medium

For a degenerate system of equations such as the equations of motion of immiscible fluids in porous media, we study the solvability of an initial–boundary value problem. Using the process of capillary imbibition of a wetting fluid as an example, we study a class of self-similar solutions with degeneration on the movable boundary and on the entry into the porous layer. The considered problem can be reduced to the analysis of properties of a nonlinear operator equation. For the classical solution of the original problem, we prove existence and uniqueness theorems.