高阶非线性Schrǒdinger方程的整体适定性

本文研究了一类非线性高阶Schrǒdinger方程Cauchy问题的整体适定性．利用不动点定理，获得了整体解的存在唯一性及解关于初值的连续依赖性和解具有较强的衰减估计．推广了文献中的结果．     

初值的导数具有紧支集的对角形双曲组Cauchy问题经典解的整体存在唯一性

本文研究了初值导数具有紧支集的对角形严格双曲组Cauchy问题在t>0上的经典解的整体存在唯一性,以及在最大特征的决定区域内的较一般的非严格双曲组的初值是在x≥0半轴上给定的,并且初值具有紧支集的Cauchy问题的经典解的整体存在唯一性.文中主要使用了特征线方法和解的一致先验估计方法.     

局部C半群与抽象Cauchy问题

在本文中，我们讨论由算子A生成的局部C半群对应的Cauchy问题，将初值x的取值范围从CD（A）推广到（λ-A）~(-1)C（E）．     

利用通量限制的高分辨Godunov型格式的熵条件

1．引言考虑非线性双曲型守恒律方程的Cauchy问题式中f（w）∈C2（R）f＂,（w）≥0,初值。u0∈BV（R）．此问题通常只存在弱解,且需附加熵条件以保证解的唯一性．方程（1.1）的数值方法研究发展很快,但一阶精度格式（如Godunov格式）分辨率很低,而二阶精度格式在间断附近存在振荡;TVD格式则是一种成功的高分辨率无振荡格式．此外,双曲型守恒律数值方法的收敛性取决于差分格式的总变差稳定和离散熵条件．文献[2]中给出了利用通量限制构造TVD格式的方法,[1]则讨论了SOR-TVD格式的熵条件．本文第2节回顾了问的方法,具体导出了…     

一类非线性渗流方程的Cauchy问题

讨论具有强非线性源和对流项的一般渗流方程以ＲＮ中某有界连续函数ｕ０（ｘ）或某一Ｒａｄｏｎ测度为初值的Ｃａｕｃｈｙ问题弱解的存在性，得到关于解的一系列重要估计．     

三维可压等熵Euler方程光滑解的整体存在性

研究了三维可压等熵Euler方程Cauchy问题光滑解的整体存在性.如果初值是一个常状态的小扰动并且初速度的旋度等于零,证明了三维可压等熵Euler方程Cauchy问题光滑解的整体存在性.     

非齐次Burgers方程周期解的大时间行为

研究非齐次Burgers方程Cauchy问题解的大时间行为.假定初值是周期的并且非齐次项具有多个零点.对初值的某些假定条件下,证明了问题的解收敛于一个行波解.所用的主要方法是广义特征线理论.     

广义Lienard方程零解的全局渐近稳定性和极限环的存在性

研究了一类广义Lienard方程 x=φ（y）,y=-f（x）φ（y）-g（x）式中φ，F，g：R→R连续且保证系统初值解惟一，给出零解全局渐近稳定性条件，并讨论极限环的存在性．     

一类非线性Schr(o)dinger方程的整体小解

本文研究带有非线性项|u|~pu的高阶非线性Schr(?)dinger方程的Cauchy问题．对于p的某一取值范围。我们证明了此问题整体解的存在唯一性,并得到了解关于初值的连续依赖性及解具有较强的衰减估计。     

方程λ＋a＋be^τλ=0全部根的精确分布

考虑方程其中a，b为任意实常数,τ为正常数．本文在复数域上求得了方程（*）全部根的精确分布．在文[1]和[2]中应用Laplace变换法，得到了滞后型方程初值问题的形式解公式下：其中x（t）为初值问题的解，这里H（θ）为Heaviside函数．方程（*）为初值问题（E）中方程的特征方程．应用本文结果于形式解公式（1．1），可求得初值问题（E）的精确解．篇幅所限，此问题另文讨论．     

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 REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

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.     

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.     

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     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with