Regularity for solutions to anisotropic obstacle problems

For Ω a bounded subset of R n,n 2,ψ any function in Ω with values in R∪{±∞}andθ∈W1,(q i)(Ω),let K(q i)ψ,θ(Ω)={v∈W1,(q i)(Ω):vψ,a.e.and v-θ∈W1,(q i)0(Ω}.This paper deals with solutions to K(q i)ψ,θ-obstacle problems for the A-harmonic equation-divA(x,u(x),u(x))=-divf(x)as well as the integral functional I(u;Ω)=Ωf(x,u(x),u(x))dx.Local regularity and local boundedness results are obtained under some coercive and controllable growth conditions on the operator A and some growth conditions on the integrand f.     

一类带临界Sobolev指数及有拟超临界Neumann边界条件的椭圆方程正解的多重性

本文讨论了Ω上如下一类带临界增长的椭圆方程在拟超临界的Neumann边界条件下正解的存在性:-Div(| u |p-2 u) =λum up*-1,-| u |p-2 u ν=ψ(x)uq-1,x∈Ω,x∈Ω.这里Ω∈RN,(N≥3)是光滑有界区域, 1≤p < N,0< m < p-1,(N -1)pN - p= p*N-1 ≤q < p*,其中p* =NpN - p是W1,p(Ω)→Ls(Ω)的Sobolev临界指数,p*N-1 =(N -1)pN - p是W1,p(Ω)→Lt( Ω)的在(N-1)维流形上的临界指数,λ>0是一个正参数.     

一类椭圆方程很弱解关于区域的连续性

本文讨论了二阶椭圆型方程-△u=f(x,u),x∈Ω的Dirichlet问题u | Ω=0的很弱解u∈W ,r(Ω)(1＜r＜2)关于区域Ω的连续性及很弱边值问题的很弱解的唯一性.     

三角代数上Lie三重导子的刻画

设u=Tri(A,M,B)是三角代数.证明了在一般的假设下,如果线性映射δ:u→u,满足对任意的U,V,W∈u且UV=UW=0(或U·V=U·W=0),有δ([[U,V],W])=[[δ(U),V],W]+[[U,δ(V)],W]+[[U,V],δ(W)],则对任意U∈u,δ(U)=φ(U)+h(U),其中φ:u→u是一个导子,线性映射h:u→Z(u),满足对任意的U,V,W∈u且UV=UW=0(或U·V=U·W=0),有h([[U,V],W])=0.     

带有位势的拟线性椭圆型方程正解的存在性

本文利用Ekeland的变分原理及山路引理,研究了以下问题在一定条件下的正解的存在性：{-△pu=λuq/|x|s+ur,u＞0,x∈Ω(∩)RN,{u(x)=0,x∈(a)Ω,其中△pu=div(| ▽ u |p-2 ▽u),u∈W1,p0(Ω),Ω是RN中的有界区域,且0∈Ω,0＜q＜p-1,N≥3,0＜s＜N(p-q-1)p-1 +q+1,p-1＜r≤p*-1,p*=Np(N-p)-1,λ＞0.此时,s可以大于p,从而推广了p=2时的某些结果.     

p(x)-Laplace方程的强极大值原理

本文给出了如下形式的p(x)-Laplace方程-div(| u|p(x)-2 u)+d(x)|u|q(x)-2u=o,x∈Ω的一个强极大值原理,其中p(x),q(x),d(x)满足一定的条件.     

On the uniqueness of the unbounded classical soultion of the evolution system describing geophysical flow within the earth and its associated systems

1. IntroductionWe consider the evolution system in Rd (d = 2, 3) as followZ -- uau 7u 7(x' V)u (u' V)u -- k(b' V)b CV(Ibl') 3W= f(X,t), (x,t) e Rd X [0,T, (1.1): -- Adb (U' V)b -- (b' V)U jVq = g(X,t), (X,t) E Rd X [0,T, (1.2)vU = 0, Vb = 0, (X, t) 6 Rd X [0,T, (1.3). U(X,0) = U0(X), b(X,0) = b0(X), X E R', (l.4)where u is the Eulerian flow velocity, p is the density; b is the magnetic field; p,q arepressures.f(x, t),g(x, t) are volume forces; u, p are constants o…     

两相可混溶驱动问题中近似压力方程的一种新方法

1　介　　绍ΩR2为凸多边形区域,Ω上的两相可混溶驱动问题可由以下微分方程系统来描述a)-.[a(x,c)(p-r(c)]=.u=q,b)φ(x)ct+u.c-(Dc)=(c-c)q=g(c),(1.1)其中a(x,c)=-k(x)μ(c),k(x)为介质的渗透率,μ(c)为流体的粘度,p为流体的压力,φ(x)为介质的孔隙度,c为一相流体的体积浓度,q为外部流体的体积流速,且满足相容性条件∫Ωqdx=0.D是2×2阶矩阵,D=φ(x)[dmI+|u|(dlE(u)+dtE⊥(u))],E(u)=(uiuj/|u|2)2×2,dm为分子扩散系数,dl,dt分别为横向、纵向弥散系数.系统的边界条件、初始条件:n为边界单位外法向a)u.n=0,(x,t)∈Ω×Jb)2i,j=1Dij(…     

散度型椭圆方程的解在Morrey空间上的细正则性

对具有不连续系数的散度型椭圆方程-(aijuxi)xj=(fj)xj的解在Morrey空间中的细正则性进行了研究,即如果aij∈VMO ∩ L∞(Ω),fj∈Lp,λ(Ω),u∈W1,q(Ω)(1＜q≤p)是方程的解,则 u∈W1,ploc(Ω)且uxj∈Lp,λloc(Ω).     

GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS FOR GENERALIZED POCHHAMMER-CHREE EQUATIONS

In this article,we study the initial boundary value problem of generalized Pochhammer-Chree equation u_(tt)-u_(xx)-u_(xxt)-u_(xxtt)=f(u) xx,x ∈Ω,t 0,u(x,0) = u0(x),u t(x,0)=u1(x),x ∈Ω,u(0,t) = u(1,t) = 0,t≥0,where Ω=(0,1).First,we obtain the existence of local W k,p solutions.Then,we prove that,if f(s) ∈ΩC k+1(R) is nondecreasing,f(0) = 0 and |f(u)|≤C1|u| u 0 f(s)ds+C2,u 0(x),u 1(x) ∈ΩW k,p(Ω) ∩ W 1,p 0(Ω),k ≥ 1,1 p ≤∞,then for any T 0 the problem admits a unique solution u(x,t) ∈ W 2,∞(0,T;W k,p(Ω) ∩ W 1,p 0(Ω)).Finally,the finite time blow-up of solutions and global W k,p solution of generalized IMBq equations are discussed.     

Wolfe线搜索下一类混合共轭梯度法的全局收敛性

本文给出了一个新的共轭梯度公式,新公式在精确线搜索下与DY公式等价,并给出了新公式的相关性质.结合新公式和DY公式提出了一个新的混合共轭梯度法,新算法在Wolfe线搜索下产生一个下降方向,并证明了算法的全局收敛性,并给出了数值例子.     

一类由概率分布生成的新度量

主要得到了一类由概率分布生成的新度量.以信息理论中的重要概念-相对熵为基础,对前人文章中的重要结论进行推广,通过利用改进的初等方法在离散的可测空间中得到了这类新度量,并且证明了得到的新度量成立的充要条件.由此再将这类新度量推广到连续的可测空间中,得到了同样的结果.最后讨论了新度量的最值问题.     

A gradient-related algorithm with inexact line searches

In this paper, a new gradient-related algorithm for solving large-scale unconstrained optimization problems is proposed. The new algorithm is a kind of line search method. The basic idea is to choose a combination of the current gradient and some previous search directions as a new search direction and to find a step-size by using various inexact line searches. Using more information at the current iterative step may improve the performance of the algorithm. This motivates us to find some new gradient algorithms which may be more effective than standard conjugate gradient methods. Uniformly gradient-related conception is useful and it can be used to analyze global convergence of the new algorithm. The global convergence and linear convergence rate of the new algorithm are investigated under diverse weak conditions. Numerical experiments show that the new algorithm seems to converge more stably and is superior to other similar methods in many situations.     

Analysis of a new parareal algorithm based on waveform relaxation method for time-periodic problems

We present a new parallel algorithm for time-periodic problems by combining the waveform relaxation method and the parareal algorithm, which performs the parallelism both in sub-systems and in time. In the new algorithm, the waveform relaxation propagator is chosen as a new fine propagator instead of the classical fine propagator. And because of the characteristic of time-periodic problems, the new parareal waveform relaxation algorithm needs to solve a periodic coarse problem at the coarse level in each iteration. The new algorithm is proved to converge linearly at most. Then the theoretic parallel efficiency of the new algorithm is also considered. Numerical experiments confirm our analysis finally.     

Supply chain dynamic configuration as a result of new product development

This study considers supply chain network configuration in an innovative environment while the new product development (NPD) will affect the supply chain configuration (SCC). The time of new product introduction has a significant effect on the market performance while it has an effect on the supply chain configuration. Supplier integration into the new product introduction is the key parameter for successfully new product introduction, which may contribute to supply chain reconfiguration. Consequently By considering the new product development concept, we may face with dynamic supply chain configuration during a planning horizontal time. In this study, a new model is presented to consider the dynamic configuration of a supply chain by developing new products. In the proposed model, the dynamic configuration of a supply chain and the new product launching time is optimized simultaneously. The proposed model considers production, sales and transportation planning for the entire supply chain in order to achieve an integrative and efficient supply as well. Then some numerical analyses have been done to show the applicability of the proposed model. The results show that the new product development has a significant effect on the configuration of supply chain.     

一种非单调滤子信赖域算法解线性不等式约束优化

本文给出了一种新的多维滤子算法结合非单调信赖域策略解线性约束优化.目标函数及其投影梯度的分量组成了新的多维滤子，并且与信赖域半径有关.当信赖域半径充分小时，新的滤子能接受试探点，避免算法无限循环.非单调信赖域策略保证了新算法的整体收敛性.目前为止，多维滤子算法局部收敛性分析仍然没有解决，在合理假设下，我们分析了新算法的局部超线性收敛性.数值结果验证了算法的有效性.     

关于解极大相关问题P-SOR算法的收敛性

对求解极大相关问题的P-SOR方法的收敛性做了进一步研究.得到了一些新的收敛条件.为了提高收敛到全局最大解的可能性,提出了一种新的初始向量选择策略.给出了P-SOR算法的对称形式(P-SSOR).还给出了一种算法精化策略.最后,用数值例子说明新方法的有效性.     

一个解大规模无约束优化问题的全局梯度法(英文)

本文提出一种新的解大规模无约束优化问题的全局收敛的梯度法.新算法沿着负梯度方向选择步长,而初始步长根据目标函数的海赛矩阵的近似数量矩阵来确定.理论上证明了新算法产生的点列的每个聚点都是稳定的,数值试验表明新算法是可靠且有效的.     

An adaptive trust region method and its convergence

In this paper, a new trust region subproblem is proposed. The trust radius in the new subproblem adjusts itself adaptively. As a result, an adaptive trust region method is constructed based on the new trust region subproblem. The local and global convergence results of the adaptive trust region method are proved. Numerical results indicate that the new method is very efficient.     

A new technique of integral representations in Cn

A new technique of integral representations in Cn, which is different from the well-known Henkin technique, is given. By means of this new technique, a new integral formula for smooth functions and a new integral representation of solutions of the -equations on strictly pseudoconvex domains in Cn are obtained. These new formulas are simpler than the classical ones, especially the solutions of the -equations admit simple uniform estimates. Moreover, this new technique can be further applied to arbitrary bounded domains in Cn so that all corresponding formulas are simplified.