Application of Relaxation Scheme to Degenerate Variational Inequalities

In this paper we are concerned with the solution of degenerate variational inequalities. To solve this problem numerically, we propose a numerical scheme which is based on the relaxation scheme using non-standard time discretization. The approximate solution on each time level is obtained in the iterative way by solving the corresponding elliptic variational inequalities. The convergence of the method is proved.     

Stability in the presence of degeneracy and error estimation

Received February 10, 1997 / Revised version received June 6, 1998 Published online October 9, 1998     

非线性退缩抛物组初边值问题解的存在性和唯一性

本文讨论一类非线性退缩抛物型方程组初边值问题广义问题广义解的存在性和唯一性。     

甲酚紫非线性光学性质的研究

报道了甲酚紫染料的非线性光学性质的实验研究方法及其结果.利用简并四波混频技术,测量得到甲酚紫甲醇溶液(浓度为5×10~(-4)M)的三阶非线性极化率X~(3)为2.0×10~(-10)esu.此外,利用不同强度皮秒脉冲相关技术得到了甲酚紫甲醇溶液的吸收恢复时间τ_(21)为163ps.     

Strong comparison principles for some nonlinear degenerate elliptic equations

In this paper, we obtain the strong comparison principle and Hopf Lemma for locally Lipschitz viscosity solutions to a class of nonlinear degenerate elliptic operators of the form ▽~2ψ + L(x, ▽ψ), including the conformal hessian operator.     

线性规划问题的一种新的摄动法

在用单纯形方法解线性规划的问题时，不可避免会出现退化情况，而某些退化情况会导致循环。目前采用的避免循环的方法一共有两类：传统的摄动法（字典序）和Bland方法。本分析了传统摄动法的一些不足，给出了一种新的摄动法。     

一类拟线性退化抛物方程的Cauchy问题

对方程α（xx）u＋uαyu-αtu=f（·,u）,（x,y,t）∈R^2×（0,T）的Cauchy问题,给出了一个整体BV-弱解的定义,证明了该弱解的连续性.     

Fixed stream-tube method for solving two-phase plane flow problems and its theoretical analysis

The fixed stream-tube method widely adopted in engineering field for giving an approximate solution to the two-dimensional problems of two-phase flow through porous media is summarized and an improvement has been made in this paper. Its core part, i.e., the fluid displacement within a one-dimensional stream tube with variable cross-sectional area under a given pressure difference across the tube is thoroughly studied. The existence and uniqueness of solution are proved, the exact solution, numerical solution and its convergence, stability analyses are given in this paper.