一类双参数非线性高阶反应扩散方程的摄动解法

研究了一类两参数非线性反应扩散奇摄动问题的模型.利用奇摄动方法,对该问题解的结构在两个小参数相互关联的情形下作了讨论.首先,构造问题的外部解; 之后在区域的边界邻域构造局部坐标系,再在该邻域中引入多尺度变量,得到问题解的边界层校正项; 然后引入伸长变量,构造初始层校正项,并得到问题解的形式渐近展开式;最后建立了微分不等式理论,并由此证明了问题的解的一致有效的渐近展开式.用上述方法得到的各次近似解,具有便于求解、精度高等特点.     

两参数非线性反应扩散积分微分方程的内层激波渐近解

研究了一类两参数非线性反应扩散积分微分奇摄动问题.利用奇摄动方法,构造了问题的外部解、内部激波层、边界层及初始层校正项,由此得到了问题解的形式渐近展开式.最后利用积分微分方程的比较定理证明了该问题解的渐近展开式的一致有效性.     

两参数非线性反应-扩散系统的尖层冲击波解

研究了一类两参数反应-扩散系统奇摄动Robin初始-边值问题.首先,利用奇摄动方法,联系到两个小参数构造了问题的外部解.其次,利用伸长变量分别得到了原问题解的的冲击波尖层,边界层和初始层校正项.最后,得到了原问题解的渐近展开式,并利用微分不等式理论证明了渐近解的一致有效性.由本方法求原问题的渐近解,它还可以进一步进行微分,积分等解析运算,从而能了解相应冲击波解的更深层的性态.因此本方法具有良好的应用前景.     

一类广义非线性反应扩散方程奇摄动问题激波解（英文）

本文研究一类广义非线性反应扩散方程奇摄动初始边值问题.首先,构造非线性问题的外部解.其次,利用局部坐标系和伸长变量得到激波层和边界层校正项.最后,利用不动点理论研究了非线性反应扩散方程初始边值问题广义解的渐近性态.     

两参数奇异摄动非线性双曲型微分系统的过渡冲击层广义解

研究了一类两参数双曲型微分系统奇异摄动初始边值问题.首先,利用奇异摄动理论和方法,注意到两个小参数,构造了问题的外部解.其次,利用多重尺度变量和伸长变量,分别得到了原问题解的过渡冲击层、边界层和初始层校正项.最后,得到了原问题解的渐近展开式,并利用泛函分析不动点理论,证明了渐近解的一致有效性.由本方法求得的原问题的渐近解,它还可以进行微分,积分等解析运算,从而能了解相应过渡冲击层解的更进一步的性态.因此本方法具有良好的应用前景.     

一类含慢变量奇摄动非线性系统初始层现象

研究含有慢变量的一类奇摄动非线性系统初始层现象,通过引进不同量级的伸长变量,构造不同“厚度”的初始层校正项,得到了摄动解关于小参数的N阶近似展开式,揭示了摄动解呈现的“层中层”现象,并利用不动点原理证明了摄动解的存在,给出了解的一致有效的渐近展开式．     

一类非线性奇异摄动自治微分系统的渐近解

研究了一类广义Lienard奇异摄动系统.首先,求出了系统的退化解;其次,利用奇异摄动方法得到了系统的外部解,并用伸长变量方法,求得了系统的初始层校正项;最后,得到了系统解的任意次渐近解析展开式,并证明了解的一致有效性.该文所用的方法和理论,具有广泛的实际应用价值.     

一类两参数非线性反应扩散方程奇摄动问题的广义解

利用奇异摄动方法讨论了一类两参数广义奇摄动反应扩散方程问题.首先,在适当的条件下,对两个小参数进行幂级数展开,构造了问题的形式外部解.其次,在区域边界邻近,建立局部坐标系,利用多重尺度变量方法分别构造了问题解的第一、第二边界层校正项.最后,利用合成展开理论,得到了问题广义解的渐近表示式,并用泛函分析不动点原理,估计了渐近展开式的精度.该文得到问题的广义解在重叠区域内具有两个不同厚度的校正函数.它们分别对边界条件起着校正的作用,扩展了问题研究范围,同时还提供了构造这类在重叠区域上不同厚度的校正项的方法,因此具有广泛的研究前景.     

具有边界摄动弱非线性反应扩散方程的奇摄动

在适当的条件下研究了一类具有边界摄动的非线性反应扩散方程奇摄动初始边值问题．首先,借助正规摄动方法,得到了原问题的外部解．其次,利用伸长变量和幂级数展开理论,构造了解的初始层项．然后,利用微分不等式理论,研究了初始边值问题解的渐近性态．最后,利用一些相关的不等式,讨论了原问题解的存在、唯一性及其一致有效的渐近估计．     

一类催化反应Robin问题的渐近解

研究了一类非线性催化反应微分方程Robin问题.在一定的条件下,先利用摄动方法求出了原Robin问题的外部解,然后用伸长变量和幂级数理论分别构造了解的第一和第二边界层校正项,从而得到了Robin问题解的形式渐近展开式.最后利用微分不等式理论,证明了问题解的渐近表示式的一致有效性.     

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.