轴对称压差系统的自相似解

考察了二维压差系统的轴对称活塞均匀膨胀而产生的自相似流动.在轴对称和自相似假设下,该问题可以简化为一个自治的非线性常微分方程组的自由边值问题.通过对常微分方程组的积分曲线性质的详细分析,建立该自由边值问题正光滑解的整体存在性.     

一类一维的辐射流体力学方程组激波的存在性

该文主要讨论一维空间中一类辐射流体力学方程组的激波. 由Rankine-Hugoniot条件及熵条件得此问题可表述为关于辐射流体力学方程组带自由边界的初边值问题. 首先通过变量代换, 将其自由边界转换为固定边界, 然后研究关于此非线性方程组的一个初边值问题解的存在唯一性. 为此先构造了此问题的一个近似解, 然后分别通过Picard迭代与Newton迭代对此非线性问题构造近似解序列. 通过一系列估计与紧性理论得到此近似解序列的收敛性, 其极限即为原辐射热力学方程组的一个激波.     

通过非均匀介质流体的渗流问题

本文讨论三维情形的渗流问题.考虑在坝体形状不规则，且介质不均匀的情况下，将渗流现象归结为线性椭圆方程的自由边值问题.应用变分不等方程理论，证明了解的存在和唯一性.     

平面弹性力学中带孔洞的自由边界含裂纹问题

本文在文献「１」、「２」的基础上提出了一类平面弹性力学中带多边形孔洞的自由边界含裂纹问题，我们先将其分解为一个解析函数的黎曼－希尔伯特边值问题和一个复方程的混合边值问题，然后利用边值问题的理论和方法，讨论了这个问题的可解性。     

具耗散项拟线性双曲型方程组的边值问题

本文考虑具耗散项一阶拟线性双曲型方程组的具有自由边界的典型自由边值问题．在一些合理假设下,证明了其经典解的整体存在性定理．     

美式期权定价问题的变网格差分方法

本文提出一种求解美式期权定价自由边值问题的变网格差分方法.通过建立一个自由边界所满足的方程,利用变网格技术可同时求出期权的差分解和最佳执行边界.本文分别讨论了显式和隐式变网格差分格式,并给出了差分解的收敛性和稳定性分析.数值实验表明本文算法是一个非常有效的期权定价算法.     

拟线性双曲型方程组典型自由边界问题的整体经典解

本文对拟线性双曲组的某些典型边值问题及典型自由边界问题,证明了整体经典解的存在唯一性。     

源于自由边值离散的弱非线性互补问题的m+1阶收敛性算法

该文通过引入基于模的非线性函数,推广了经典牛顿算法,构造了一个具有高阶收敛性的加速牛顿法来求解一类源于自由边值问题离散的弱非线性互补问题.理论上详细地分析了其收敛效率.数值实验充分验证了所提出算法的可行性和有效性.     

偏微分方程的函数论方法及应用和计算

本文主要介绍了偏微分方程一些边值问题的函数论方法。首先给出了边值问题的适定提法；其次研究了多复变函数、Ｃｌｉｆｆｏｒｄ代数、某类抛物型方程、一些复合型方程组和双曲型方程组各种边值问题的可解性；进而使用一阶椭圆型方程组间断边值问题的结果，解决了渗流理论、空气动力学与弹性力学中提出的若干自由边界问题；最后还讨论了某些椭圆边值问题与拟共形映射的近似解法。从此文可以看出；函数论方法在处理偏微分方程的一些优     

一类弧形弹性杆大变形的多解性与分支

基于大变形理论建立弧形弹性杆大变形的数学模型,弹性杆的一端固定,另一端自由且在中间受一竖直向下的集中力,所建立的模型可变形为摆动方程的边值问题.利用流形法得到数学模型的分支图,进而分析弹性杆变形的多解性.     

拉单晶问题差分解的收敛性

本文考虑一源于拉单晶热传导数学模型的三角形区域上的自由边界问题的数值解，给出差分格式，并证明其数值解的收敛性。     

REGULARITY OF THE FREE BOUNDARY IN ELECTROCHEMICAL MACHINING PROBLEM

ＲＥＧＵＬＡＲＩＴＹＯＦＴＨＥＦＲＥＥＢＯＵＮＤＡＲＹＩＮＥＬＥＣＴＲＯＣＨＥＭＩＣＡＬＭＡＣＨＩＮＩＮＧＰＲＯＢＬＥＭＹｕａｎＧｕａｎｇｗｅｉ（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＰｈｙｓｉｃｓａｎｄＣｏｍｐｕｔａｔｉｏｎａｌＭａｔｈｅｍａｔｉｃｓ...     

THE GLOBAL ARTIFICIAL BOUNDARY CONDITIONS FOR NUMERICAL SIMULATIONS OF THE 3D FLOW AROUND A SUBMERGED BODY

We consider the numerical approximations of the three-dimensional steady potential flow around a body moving in a liquid of finite constant depth at constant speed and distance below a free surface in a channel. One vertical side is introduced as the up-stream artificial boundary and two vertical sides are introduced as the downstream arti-ficial boundaries. On the artificial boundaries, a sequence of high-order global artificial boundary conditions are given. Then the original problem is reduced to a problem defined on a finite computational domain, which is equivalent to a variational problem. After solving the variational problem by the finite element method, we obtain the numerical approximation of the original problem. The numerical examples show that the artificial boundary conditions given in this paper are very effective.     

A NUMERICAL METHOD FOR DETERMINING THE OPTIMAL EXERCISE PRICE TO AMERICAN OPTIONS

American Options can be exercised prior to the date of expiration,the valuation of American options then constitutes a free boundary value problem.How to determine the free boundary,i.e. the optimal exercise price,is a key problem.In this paper,a nonlinear equation is given.The free boundary can be obtained by solving the nonlinear equation and the numerical results are better.     

THE REGULARITY OF THE FREE BOUNDARY FOR STRIKE RESET OPTION

A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a parabolic variational inequality and the optimal reset strategy is the free boundary. The smoothness of the free boundary in some cases was showed in our article published in JDE. We would prove its smoothness in the other case in this paper by a generalized comparison principle for the variational inequality.     

GLOBAL SOLUTIONS TO THE NAVIER-STOKES EQUATIONS FOR COMPRESSIBLE HEAT-CONDUCTING FLOW WITH SYMMETRY AND FREE BOUNDARY

ABSTRACT

Global solutions of the multidimensional Navier-Stokes equations for compressible heat-conducting flow are constructed, with spherically symmetric initial data of large oscillation between a static solid core and a free boundary connected to a surrounding vacuum state. The free boundary connects the compressible heat-conducting fluids to the vacuum state with free normal stress and zero normal heat flux. The fluids are initially assumed to fill with a finite volume and zero density at the free boundary, and with bounded positive density and temperature between the solid core and the initial position of the free boundary. One of the main features of this problem is the singularity of solutions near the free boundary. Our approach is to combine an effective difference scheme to construct approximate solutions with the energy methods and the pointwise estimate techniques to deal with the singularity of solutions near the free boundary and to obtain the bounded estimates of the solutions and the free boundary as time evolves. The convergence of the difference scheme is established. It is also proved that no vacuum develops between the solid core and the free boundary, and the free boundary expands with finite speed.     

SOLVABILITY OF A PARABOLIC-HYPERBOLIC TYPE CHEMOTAXIS SYSTEM IN 1-DIMENSIONAL DOMAIN

In this paper, we use contraction mapping principle, operator-theoretic approach and some uniform estimates to establish local solvability of the parabolic-hyperbolic type chemotaxis system with fixed boundary in 1-dimensional domain. In addition, local solvability of the free boundary problem is considered by straightening the free boundary.     

亚热带高原湖泊水质方程一类自由初边值问题

亚热带高原湖泊除了有来自工业、农业，生活污水及落尘的外部污染，还有来自湖泊藻类水生生物循环及底泥的污染物释放内污染源污染。因此，由于进出水量不均衡性导致湖水边界的自由变动。本文首先运用微元分析法导出在外源和内源双重污染下湖泊水质模型，然后对一类自由初边值问题通过对非柱形边界条件的齐次约化，运用变分型算子的向量扩张和拟单调方法获得解的存在性、唯一性。     

LOCAL CLASSICAL SOLUTION OF FREE BOUNDARY PROBLEM FOR A COUPLED SYSTEM

This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-lnaintaining protocell in multidimensional case. The local classical solution of the problem with free boundary F : y = g(x,t) between two domains is being seeked. The local existence and uniqueness of the problem will be proved in multidimensional case.     

A STUDY OF THE PROFITABILITY FOR AN OPTIMAL CONTROL PROBLEM WHEN THE SIZE OF THE DOMAIN CHANGES

ABSTRACT. In this work we consider the increase in benefit for a control problem when the size of domain increases. Our control problem involves the study of the profitability of a biological growing species whose growth is confined to a bounded domain Ω? R^N and is modeled by a logistic elliptic equation with different boundary conditions (Dirichlet or Neumann). The payoff-cost functional considered, J, is of quadratic type. We prove that, under Dirichlet boundary conditions, the optimal benefit (sup J) increases when the domain ? increases. This is not true under Neumann boundary conditions.