关于一类非线性发展方程整体解的存在性问题

本文研究一类模拟非线性弹性杆的纵振动的非线性发展方程的初边值问题，证明了其整体解的存在性、唯一性、光滑性及在一定条件下，整体解的不存在性。     

关于一阶拟线性方程的整体解

对于非线性偏微分方程,通常局部可解性比较容易得到,而整体解问题则复杂得多.近年来,关于非线性偏微分方程的整体可解性已得到很多研究结果.比如[1]、[2]中讨论了非线性波动方程的整体可解性.[3]中讨论了某种双曲型方程组的整体可解性.[4]中讨论了某种非线性椭圆型方程的整体不可解性.也有大量工作讨论整体广义解的存在性.这些结果都是关于微分方程的初值问题或边值问题的整体可解性.但是如果我们期望得到全空间的整体解,那么如本文所得到的结果那样,微分方程本身是否存在这种整体解就是一个很值得研究的问题. 我们称方程的在全空间具有直到方程阶数的连续导数的解为全正则解.     

一类带非线性边界条件的非线性抛物方程的解的整体存在性

该文考虑带非线性边界条件的非线性抛物方程的正整体解的存在性与非存在性。通过使用上下解技巧，得到了所有正解整体存在的充分必要条件。作者所构造的上下解具有相同的形式且计算简便。     

第25卷B辑第4期(2004)目次和提要

非线性弹性动力学方程组在星形域外Dirichlet型初边值问题解的几乎整体存在性 辛杰 秦铁虎 该文讨论非线性弹性动力学方程组在星形域外的Dinchlet型初边值问题,对小初值证明了该问题解的几乎整体存在性,给出解的生存区间的下界.     

一类多重非线性抛物方程组解的整体不存在性

本文研究了一类多重非线性抛物方程组初边值问题解的整体不存在性,利用修正的能量扰动法,得到了正初始能量解的整体不存在性结果.     

一类非线性积分微分方程的初边值问题

本文讨论下列初边值问题整体经典解的存在性：该问题所描述的是一类具有非线性粘弹性的粘弹性杆的非线性振动，在一定条件下，我们证明了该问题整体经典解的存在唯一性。     

具奇系数发展型p-Laplace不等方程整体解的不存在性

考虑两类带奇性系数发展型p-Laplace不等方程整体非负解的不存在性,也即要证明某些拟线性抛物型方程的非线性Liouville定理.通过先验估计,证明了整体解在某个带参数的函数空间中的不存在性.当只考虑连续整体解时,可选取不带参数的函数空间并证明整体解在其中的不存在性.     

具奇系数发展型p-Laplace不等方程整体解的不存在性

考虑两类带奇性系数发展型p-Laplace不等方程整体非负解的不存在性,也即要证明某些拟线性抛物型方程的非线性Liouville定理．通过先验估计,证明了整体解在某个带参数的函数空间中的不存在性．当只考虑连续整体解时,可选取不带参数的函数空间并证明整体解在其中的不存在性．     

非线性高阶抛物双曲型耦合方程组的第一边界问题

本文研究了一类广义Sine-Gordon型非线性高阶双曲方程组、非线性高阶拟双曲型方程组、非线性高阶拟抛物型方程组以及非线性高阶广义Sehrdinger型方程组的耦合方程组的第一边界问题,作者证明了此耦合方程组第一边界问题的整体广义解和整体古典解的存在性、唯一性和光滑性。     

方程Utt—△Ut=f（u）的整体解

本文用Galerkin方法研究多维非线性拟双曲方程u_(tt)-Δu_t=f(u)的初边值问题与初值问题的整体广义解的存在性及整体强解的存在和唯一性,得到了与对应的非线性波动方程截然不同的很有意义的结果。这一结果从一个方面充分体现了非线性拟双曲方程与非线性双曲方程根本不同的特征。     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.