微分算子和边界双摄动的高阶椭圆型方程的狄立克雷问题

本文研究了在边界和算子摄动相结合的情况下高阶椭圆型方程解的渐近式的构造.如果非摄动问题A₀不在谱上,则摄动问题A_ε的渐近解可按小参数ε的次幂展开;如果A₀在谱上,则在A_ε的渐近解中出现有小参数ε的负幂;同时给出了有关的余项的估计.     

小参数常微分方程守恒型差分格式的一致收敛性

本文考虑自共轭常微分方程奇异摄动边值问题,构造一族带拟合因子的差分格式,给出差分格式解一致收敛于微分方程解的充分条件,由此提出几个具体格式,在条件较弱的情况下,给出较高的一致收敛阶。     

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.     

关于钱氏摄动法的高阶解的计算机求解和收敛性的研究

本文借助于中心受集中载荷圆板小挠度问题的积分方程,获得了摄动参数为中心挠度的任意n阶摄动解的解析式.于是,任意次摄动解的所有待定系数能用计算机求解.因此,获得了相当高阶的摄动解.在此基础上,讨论了钱氏摄动法的渐近性和适用区.     

函数不连续的二阶拟线性奇摄动边值问题

讨论了函数不连续情况下二阶拟线性奇摄动边值问题,用边界层函数法和轨道的光滑缝接,构造了问题的形式渐近解,并在整个区间上证明了形式渐近解的一致有效性,把吉洪诺夫系统中的函数光滑条件推广到了不连续情况.     

变截面圆形管道粘性流动的伽辽金-摄动杂交解

采用伽辽金-摄动杂交法来研究壁面是正弦形状的变截面圆形管道的粘性流动,从而避免了摄动小参数的局限性和单纯伽辽金法基函数选取的任意性的困难．讨论了边界和雷诺数对流动的影响,获得流动分离点和附着点的位置,还分析了壁面剪应力和摩擦系数沿轴向的变化情况．在小参数的情况下,计算所获得的结果与摄动解吻合良好．     

板和扁壳大挠度问题摄动参数的最小二乘法选择

本文提出了在用摄动法求解板和扁壳轴对称大挠度问题时,确定摄动参数的最小二乘方法.计算了圆板情形的算例,与准确解和其它摄动解做了比较.结果表明,本文解答较其它摄动解有更高的精确度.     

基于摄动法的压敏储层非线性渗流问题研究

研究地层压力变化对渗流特征的影响,对低渗透储层、碳酸盐岩储层,或其他致密性储层的油气开采和储层改造都具有重要意义.在考虑渗流压力梯度平方项存在的前提下,运用摄动法求解的相关理论,将渗透率随压力的变化融入到渗流问题的求解过程中,有效地求解了该类压敏型储层的非线性渗流问题.结果表明,在实际应用中,尤其是在储层压敏性较弱的情况下,可考虑直接用0阶摄动解即可满足较好的计算精度;储层的压敏性越强,越适宜通过用摄动解的修正,来达到精确求解的目的.     

具有非局部反应的时滞扩散Nicholson方程的行波解

对具有扩散项的时滞Nicholson方程的行波解进行了研究．特别是考虑到生物个体在空间位置上的迁移,研究了具有非局部反应的时滞扩散模型．对于弱生成时滞核,运用几何奇异摄动理论,在时滞充分小的情况下,证明了行波解的存在性．     

具有非局部反应的时滞扩散Nicholson方程的行波解

对具有扩散项的时滞Mcholson方程的行波解进行了研究.特别是考虑到生物个体在空间位置上的迁移,研究了具有非局部反应的时滞扩散模型.对于弱生成时滞核,运用几何奇异摄动理论,在时滞充分小的情况下,证明了行波解的存在性.     

一个新的稳定性判据

本文得到了一个常系数线性差分方程组零解渐近稳定的新判据。     

The large time behavior of solutions of a diffusion equation involving a nonlocal convection term

We study the existence, uniqueness, and asymtotic behaviour of non-negative solutions to a parabolic diffusion equation involving a nonlocal con-vective term on a bounded domain ? contained in Rⁿ. We apply the In variance Principle of LaSalle and Hale to prove that the solution tends to zero as t → ∞     

泛函微分方程安全全局渐近稳定性的一类判别准则

本利用分离变量型V函数，建立了泛函微分方程安全全局渐近稳定性的一类Razumikhin型定理，并对一类变时滞线性微分差分方程给出简明的安全全局渐近稳定性判别准则。     

Asymptotic limits of a self-dual Ginzburg–Landau functional in bounded domains

In the author's joint paper [HJS] with Jost and Struwe, we discuss asymtotic limits of a self-dual Ginzburg–Landau functional involving a section of a line bundle over a closed Riemann surface and a connection on this bundle. In this paper, the author generalizes the above results [HJS] to the case of bounded domains. Received: 20 June 1997     

Error estimates for Gaussian quadrature formulae

Summary We derive both strict and asymtotic error bounds for the Gauss-Jacobi quadrature formula with respect to a general measure. The estimates involve the maximum modulus of the integrand on a contour in the complex plane. The methods are elementary complex analysis.     

非线性联立方程模型的充分信息最大加权似然估计及其性质

提出非线性联立方程模型的充分信息最大加权似然估计并得到其一致性和渐近正态性的大样本性质 .     

变系数高阶中立型泛函微分方程的振动性与渐近性

考虑变系数高阶中立型泛函微分方程 在—10的限制,改进以往的相应结果。本文结果对高阶泛函方程x~((n))(t) p_i(t)x(t—τ_i(t))=0也是适用的。     

Essential and continuous spectrum of symmetric difference equations

Essential and continuous spectrum of symmetric difference equations have been investigated. It has been shown that the deficiency indices and the existence of these components of the spectrum are determined by the growth conditions of the coefficients. In particular, the deficiency indices are superimposition of those clusters determined by the coefficient growth. Finally, we have proved the neccessary and sufficient conditions for the existence of essential spectrum of selfadjoint subspace extensions using subspace theory and asymtotic summation.     

Asymptotics of the spectrum of a second-order nonselfadjoint degenerate elliptic differential operator on the interval

Some properties are studied of a degenerate elliptic operator P defined on the interval (0, 1); namely, the resolvent of P is estimated. The completeness is investigated of the system of vector functions of P, and the summability is studied by the Abel method with parentheses of the Fourier series of elements in the corresponding Hilbert spaces with respect to systems of the root vector functions of P. An asymtotic formula is obtained for the distribution of the eigenvalues of P that distinguishes the principal term of the asymptotics.     

An asymptotic bound for the complexity of monotone graph properties

We present an application of the topological approach of Kahn, Saks and Sturtevant to the evasiveness conjecture for monotone graph properties. Although they proved evasiveness for every prime power of vertices, the best asymtotic lower bound for the (decision tree) complexity c(n) known so far is ¼n ², proved in the same paper. In case that the evasiveness conjecture holds, it is ½n(n?1).We demonstrate some techniques to improve the 1/4 bound and show $ c(n) \geqslant \tfrac{8} {{25}}n^2 - o(n^2 ) We present an application of the topological approach of Kahn, Saks and Sturtevant to the evasiveness conjecture for monotone graph properties. Although they proved evasiveness for every prime power of vertices, the best asymtotic lower bound for the (decision tree) complexity c(n) known so far is ?n ², proved in the same paper. In case that the evasiveness conjecture holds, it is ?n(n−1).We demonstrate some techniques to improve the 1/4 bound and show $ c(n) \geqslant \tfrac{8} {{25}}n^2 - o(n^2 ) $ c(n) \geqslant \tfrac{8} {{25}}n^2 - o(n^2 ) .