四阶具强阻尼非线性波动方程解的整体存在性与不存在性

研究四阶具强阻尼非线性波动方程utt-△u+△2u-α△ut=f(u)的初边值问题.利用位势井方法,得到了问题整体解存在性与不存在性的最佳条件(门槛结果).     

四阶具强阻尼非线性波动方程解的整体存在性与不存在性

研究四阶具强阻尼非线性波动方程utt-△u+△~2u-α△ut=f(u)的初边值问题.利用位势井方法,得到了问题整体解存在性与不存在性的最佳条件(门槛结果).     

非线性Klein-Gordon方程柯西问题解的整体存在性与Blow-up

研究非线性Klein-Gordon方程的柯西问题u_(tt)-Δu+u=u|u|~(p-1),x∈R~n,t>0;u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈R~n.通过引进一族位势井,得到了解的整体存在性与不存在的门槛结果.     

具阻尼的高维广义Boussinesq方程的Cauchy问题的整体适定性

研究了一类具阻尼的高维广义Boussinesq方程u_(tt)-△u-△u_(tt)+△~2u-k△u_t=△f(u)的Cauchy问题.在没有建立问题局部解存在性理论的情况下,利用位势井方法分析了阻尼系数k与初值及井深之间的关系,得到了整体解存在与不存在的门槛结果.     

具有阻尼的半线性波动方程解的衰减估计

研究具有阻尼的半线性波动方程的初边值问题u_(tt)-△u+βu_t=|u|~(p-1)u,x∈Ω,t>0u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈Ωu|_((?)Ω)=0,t≥0其中γ为正常数,Ω■R~n为有界域,当n≥3时,1相似文献   

一类非线性发展方程整体弱解的存在性和稳定性

该文考虑一类新的非线性方程(｜ut｜r-2ut)t-Δutt-Δu-ρ(t)Δut=f(u) 的初边值问题，利用小扰动法证明了整体弱解的 存在性，借用位势井的概念得到了解的稳定性.〖HT5”H〗关键词:〖HT5”SS〗非线性发展方程;初边值问题;整体弱解;稳定性.     

具组合型非线性项与调和位势的非线性Schr(o)dinger方程

讨论了一类带有组合型非线性项与调和位势的非线性Schr(o)dinger方程.通过构造变分问题,引入位势井方法.给出了位势井的结构和位势井深度函数的性质.得到了问题的相关集合在流之下的不变性.揭示了只要问题的初值属于位势井内或位势井外,则问题在今后所有时间内的解都存在于位势井内或井外.结合凹性方法,给出了解的整体存在性的最佳条件.     

具有多个非线性源项的波动方程

利用位势井方法研究在有界区域上具有多个非线性源项的波动方程初边值问题．给出了位势井的结构和位势井深度函数的性质．通过引进位势井族得到了在这些问题的流之下的一些集合不变性以及解的真空隔离,揭示了只要问题的初值属于位势井内或位势井外,则问题在今后所有时间内的解都存在于位势井内或井外,同时存在一个没有解的空间区域．进而给出了解的整体存在和不存在的门槛结果．最后,利用相同的方法讨论了具有临界初始条件的问题．     

具有阻尼项的非线性KG方程的柯西问题

首先,介绍位势井及位势井族,并由定义证明其性质;其次,证明整体解的不变性;最后得到了整体解的存在定理,并得到了有限时间内解的爆破.     

基于交叉变分的非线性Klein—Gordon方程解的整体存在和爆破

研究非线性Klein-Gordon方程的初边值问题,运用位势井方法,在E(0)d的情况得到了方程解的整体存在和爆破.在临界能量状态得到了整体解的存在性与不存在性.最后使用凸性方法,得到某些具有高初始能量解的爆破.     

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.