Navier-Stokes-Fourier方程的可压逼近

该文利用人工可压逼近方法来研究不可压的Navier-Stokes-Fourier方程的逼近问题.首先引进扰动的可压Navier-Stokes-Fourier方程族,当∈→0~+时,其逼近不可压的NavierStokes-Fourier方程.其次给出了扰动的可压Navier-Stokes-Fourier方程解的存在性并证明其收敛到不可压的Navier-Stokes-Fourier方程的解.     

具非自治微小扰动的脉冲方程三个古典解的存在性

在半直线无穷区间上,我们研究具有微小非自治扰动项的脉冲方程边值问题的古典解,应用变分方法和相应的临界点理论得到了三个古典解的存在性.     

Langmuir扰动方程和Zakharov方程:光滑性与近似

考虑了一类带参数H,用于描述Langmuir扰动的方程.研究了当参数H趋于0时,这一类扰动方程的渐近行为.通过建立一个弱收敛结果和一个强收敛结果,得到了这类扰动方程初值问题的解(EH,nH)收敛到Zakharov方程初值问题的解(E,n)的结论.     

带小扰动的随机发展方程的不变测度

本文考虑带小扰动的随机发展方程,证明如何建立此方程的耦合解.作为应用,我们证明解的Feller连续性和不变测度的存在唯一性.还进一步建立了当扰动趋于零时,关于这族不变测度的大偏差原理.     

迁移方程的扩散近似的收敛性

导出了迁移方程的扩散近似方程．说明了它的离散纵标方法在区间内和边界上都有扩散极限，它的解关于一致地收敛于迁移方程的解．其收敛性的证明是依据其渐近扩散展开式，在边界层上得到的误差估计逼近其离散纵标方法的解．     

奇异积分方程解的稳定性

该文在[1]的基础上，进一步探讨了区间[－1，1]上带Cauchy核奇异积分方程权函数的分解及其解的稳定性和在Chebyshev模下的稳定性条件．证明了扰动方程的可解性及原方程的解对于已知函数的连续依赖性．     

自反严格凸Banach空间中约束极值解问题的扰动分析

借助于代数度量广义逆方面的扰动结论,同时利用一般的约束极值解问题和无约束极值问题的一个等价转化,该文在自反严格凸Banach空间中获得了具有等式约束的极值解问题的扰动估计.最后,作为主要结论的推论,该文分别考虑了不适定算子方程的极值解、最佳逼近解和点投影到线性流形等问题的扰动分析.     

一组带扰积分算子M-P逆的抗扰投影逼近

本文研究了一类算子方程及其扰动系统计算格式面临的格式扰动问题.利用最小二乘投影的方法,获得了最佳逼近解的投影近似格式经得起稳定扰动取决于λ的选取这一结果.推广了从特殊算子到一般有限秩算子这一结果.     

无穷区间上一类不连续非线性积分方程的唯一解

在一般Banach空间中研究了一类无穷区间上不连续非线性积分方程的唯一解．在非常弱的条件下证明了非线性积分方程的唯一解可以由迭代序列的一致极限得到，并给出了逼近解的迭代序列的误差估计式，然后应用到无穷区间一阶微分方程的终值问题，本质改进（将紧型条件删去）并推广了一些结果．     

半直线上的Hammerstein积分方程的有限截段逼近

在半直线上线性积分方程:的数值求解中,用方程(0.1)相应的有限截段方程的解、x_m(s)逼近原方程的解x(s)的方法得到x_m对x在有限区间上的一致收敛性结果.用这种方法研究方程(0.1)的数值解日见增多,特别是在[1]中,Anselone与Sloan提出所谓点列的“严格收敛性”概念来研究方程(0.1)与(0.2)的关系,显著地改     

On the initial layer and the existence theorem for the nonlinear Boltzmann equation

The truncated Hilbert expansion including the initial layer terms is considered. This enables us to replace the singulary perturbed Boltzmann equation by a weakly nonlinear equation. In this way the existence of a strong solution of the Boltzmann equation is obtained for initial data close enough to a local Maxwellian. The solution exists in the physically significant time interval on which smooth solutions to the Euler equations exist.     

Perturbation theory for mathematical programming problems

Mathematical programming (MP) problems depending on a small parameter are investigated. Attention is paid to the cases where the solutions to the reduced program and/or the solutions to the dual reduced program are not unique. Conditions are given for the convergence of perturbed solutions to a point of the reduced problem solution set, if the small parameter tends to zero. It is shown how to find this point and how to construct an approximate solution to the perturbed program. A singular situation may appear if the dual solution set is unbounded. In this case, a gap between perturbed and reduced solutions may arise. However, it is shown that the perturbed solutions are close to the solutions of some modified reduced problem. The practical usefulness of perturbation theory is demonstrated by considering the two LP problems. Decomposition and aggregation procedures are constructed on the base of general results to find suboptimal solutions of these problems.     

奇摄动问题中阶梯状解的缝接法

In view of singularly perturbed problems with complex inner layer phenomenon,including contrast structures(step-step solution and spike-type solution),corner layer behavior and right-hand side discontinuity,we carry out the process with sewing connection.The presented method of sewing connection for singularly perturbed equations is based on the two points singularly perturbed simple boundary problems.By means of sewing orbit smoothness,we get the uniformly valid solution in the whole interval.It is easy to prove the existence of solutions and deal with the high dimensional singularly perturbed problems.     

一类非线性奇摄动方程的激波问题

利用奇摄动理论和匹配原理，讨论了一类非线性奇摄动方程的激波问题．首先，构造了原问题的外部解和内层解．其次，研究了当激波在区间的边界附近和内部的激波解．最后，得出了与边界条件相对应的激波位置及解的表达式．     

Dynamics of the nonlinear stochastic heat equation with singular perturbation

The approximation in probability for a singular perturbed nonlinear stochastic heat equation is studied. First the approximation result in the sense of probability is obtained for solutions defined on any finite time interval. Furthermore it is proved that the long time behavior of the stochastic system is described by a global random attractor which is upper semi-continuous with respect to the singular perturbed parameter. This also means the long time effectivity of the approximation with probability one.     

On singular perturbations for differential inclusions on the infinite interval

We consider a differential inclusion subject to a singular perturbation, i.e., part of the derivatives are multiplied by a small parameter >0. We show that under some stability and structural assumptions, every solution of the singularly perturbed inclusion comes close to a solution of the degenerate inclusion (obtained for =0) when tends to 0. The goal of the present paper is to provide a new result of Tikhonov type on the time interval [0,+∞[.     

Componentwise fast convergence in the solution of full-rank systems of nonlinear equations

The asymptotic convergence of parameterized variants of Newton’s method for the solution of nonlinear systems of equations is considered. The original system is perturbed by a term involving the variables and a scalar parameter which is driven to zero as the iteration proceeds. The exact local solutions to the perturbed systems then form a differentiable path leading to a solution of the original system, the scalar parameter determining the progress along the path. A path-following algorithm, which involves an inner iteration in which the perturbed systems are approximately solved, is outlined. It is shown that asymptotically, a single linear system is solved per update of the scalar parameter. It turns out that a componentwise Q-superlinear rate may be attained, both in the direct error and in the residuals, under standard assumptions, and that this rate may be made arbitrarily close to quadratic. Numerical experiments illustrate the results and we discuss the relationships that this method shares with interior methods in constrained optimization. Received: September 8, 2000 / Accepted: September 17, 2001?Published online February 14, 2002     

一类非线性快慢系统非局部问题的摄动解

主要讨论了一类非线性快慢系统非局部问题的摄动解,在适当的条件下,根据不同边界层利用伸长变量和幂级数展开理论,构造了问题的形式渐近解,并利用微分不等式理论在整个区间上证明了形式渐近解的一致有效性,把奇摄动问题的摄动解推广到快慢系统非局部问题的摄动解.     

On the Evolution Operator of the Gradient Diffusion Hierarchy for Plane Rotators

By using a high-temperature cluster expansion, we construct the evolution operator of the BBGKY-type gradient diffusion hierarchy for plane rotators that interact via a summable pair potential in a Banach space containing the Gibbs (stationary) correlation functions. We prove the convergence of this expansion for a sufficiently small time interval. As a result, we prove that weak solutions of the hierarchy exist in the same Banach space. If the initial correlation functions are locally perturbed Gibbs correlation functions, then these solutions are defined on an arbitrary time interval.     

Perturbations of Dynamic Equations

We give conditions on the coefficient matrix for certain perturbed linear dynamic equations on time scales ensuring that there exists a bounded solution (which is explicitly given) to which all other solutions converge, and similarly conditions ensuring a bounded solution from which all other solutions diverge. We also consider periodic time scales and corresponding linear dynamic equations with periodic coefficients and prove similar statements about periodic solutions to which all other solutions converge or from which all other solutions diverge.