A LIOUVILLE THEOREM FOR STATIONARY INCOMPRESSIBLE FLUIDS OF VON MISES TYPE

We consider entire solutions u of the equations describing the stationary flow of a generalized Newtonian fluid in 2 D concentrating on the question, if a Liouville-type result holds in the sense that the boundedness of u implies its constancy. A positive answer is true for p-fluids in the case p 1(including the classical Navier-Stokes system for the choice p = 2), and recently we established this Liouville property for the Prandtl-Eyring fluid model,for which the dissipative potential has nearly linear growth. Here we finally discuss the case of perfectly plastic fluids whose flow is governed by a von Mises-type stress-strain relation formally corresponding to the case p = 1. It turns out that, for dissipative potentials of linear growth, the condition of μ-ellipticity with exponent μ 2 is sufficient for proving the Liouville theorem.     

关于椭圆型方程解的Liouville定理

在ｂ（ｘ）的较弱条件下，对下面的椭圆型方程，证整解的Ｌｉｏｕｖｉｌｌｅ 定理成立。     

Carnot群上一类半线性方程的Liouville型定理

本文研究了Carnot群上一类具有超线性非齐次项的半线性次Laplace方程非负解的存在性问题.结合Birindelli等[4]在Heisenberg群上利用积分不等式研究解的方法和拟齐性分析技巧,给出了此类方程在Carnot群上的一类Liouville型定理.     

SOME LIOUVILLE TYPE THEOREMS FOR THE P-SUB-LAPLACIAN ON THE GROUP OF HEISENBERG TYPE

In this paper we prove some Liouville type results for the p-sub-Laplacian on the group of Heisenberg type. A strong maximum principle and a Hopf type principle concerning p-sub-Laplacian are established.     

一类Fuchs型方程的椭圆正则性定理

本文研究了一类锥Sobolev空间上的Fuchs型方程的解的性态,利用Bony的仿微分算子理论的方法,运用仿积、仿复合、仿线性化等工具,并结合Mellin象征的性质,得到了此类方程的椭圆正则性定理.推广了在经典Sobolev空间中的椭圆正则性结果.     

LIOUVILLE TYPE THEOREMS OF SEMILINEAR EQUATIONS WITH SQUARE SUM OF VECTOR FIELDS

Let Xj,j=1,…k,be first order smooth quasi-homogeneous vector fields on R^n with the property that the dimension of the Lie algebra generated by these vector fields is n at x =0 and Xj^*--Xj,j=1,…,k,Let L=∑i=1^k Xi^2,In this paper,we study the nonnegative solutions of semilinear equation.     

INERTIAL ALGORITHMS FOR THE STATIONARY NAVIER-STOKES EQUATIONS

Several kind of new numerical schemes for the stationary Navier-Stokes equations based on the virtue of Inertial Manifold and Approximate Inertial Manifold, which we call them inertial algorithms in this paper, together with their error estimations are presented. All these algorithms are constructed under an uniform frame, that is to construct some kind of new projections for the Sobolev space in which the true solution is sought. It is shown that the proposed inertial algorithms can greatly improve the convergence rate of the standard Galerkin approximate solution with lower computing effort. And some numerical examples are also given to verify results of this paper.     

描述地球物理流动的磁流体型发展方程定常解的Lr指数稳定性

本文证明了R^n(n=2,3)中有界区域上描述地球物理流动的磁流体型发展方程的定常解的存在唯一性，在外力满足适当的条件下，证明了任何非定常的L^r(r≥2）有界解当t→∞时按指数次幂趋于定常解。     

定常Navier-Stokes方程有限元分析

的近似解.方程(1.1)中的Γ是区域Ω(R~N)的边界.假设Γ充分光滑,在适当条件下,上述问题的解(u,p)(∈(H_0~1)(Ω))~N×L_0~2(Ω))是存在唯一的.关于H_0~1(Ω),L_0~2(Ω)等记号将在下面统一说明.Falk曾用Galerkin-Langrange乘子法找Stokes问题的近似解,近似解空间(V_(1h)~0)~N×X_h取为(H_0~1(Ω))~N×L~2(Ω)的有限维子空间.[3]中指出,当Ω不是多角形区域时,构造H_0~1(Ω)且满足一定条件的有限维子空间V_(1h)~0是比较复杂     

LIOUVILLE RESULTS FOR STABLE SOLUTIONS OF QUASILINEAR EQUATIONS WITH WEIGHTS

This paper is devoted to the quasilinear equation ■where p 2,Ω is a(bounded or unbounded) domain of R~N,w_1,w_2 are nonnegative continuous functions and f is an increasing function. We establish a Liouville type theorem for nontrivial stable solutions of the equation under some mild assumptions on Ω,w_1, w_2 and f, which extends and unifies several results on this topic.     

关于PDAOR算法的广义STEIN—ROSENBERG型定理

1．引言众所周知，许多微分方程（组）经过有限差分或有限元离散，均可归结为大型分块线性代数方程组的数值求解问题，这里n。（5。5N）为给定的N个正整数，满足Zn。＝n．为利用多处理机系统有效而准t’z＝1确地得到JI．n的近似解．诵过合理地分解系统〔1．1），并有机地运用加速超松弛技术，【11提出了一类新的求解大型分块线性代数方程组（1．1）的并行分解型加速超松弛迭代算法，即PDAOR－一算法．这类算法具有很强的并行功能和良好的数值性质．大量数值实验表明，较之经典的AOR算法，PDAOR－一算法具有更快的收敛速度，更大的收…     

二阶中立型微分方程振动比较定理

首先建立了一个Ｐｉｃｏｎｅ型的恒等式及两个Ｓｔｕｒｍ型的比较定理。利用它们定量地给出一类二阶中立型微分方程所有解振动的充分条件，著名的关于二阶常微分方程的Ｓｔｕｒｍ基本定理为本文定理之特例。     

光滑平稳高斯过程极值几乎处处极限定理的一个推广

本文研究了连续均方可微的平稳高斯过程的极限性态. 通过选择一个不同于Tan (2013) 的权重函数, 在较弱的条件下得到了连续均方可微平稳高斯过程极值的一个几乎必然仅限定理, 推广了Tan(2013) 的结论.     

EXTENDABILITY OF SOLUTIONS FOR THE LINEAR SYSTEM OF ELLIPTIC TYPE EQUATIONS

The solutions of linear system of elliptic type equations with first order isdiscussed by using the method of several complex analysis and, a series of newextended results of the solutions for the system of elliptic type are obtained.     

Sobolev型方程有限元的后处理方法

1 引言 考虑下述Sobolev型方程的混合问题 (a) (b) (c) 其中Ω为R~2中具有边界的矩形域,a,b,f,u_o。为适当光滑且有界的已知函数,a(x,t)有正下界a_*. Sobolev型方程是重要的数学物理方程之一,文[1]导出了问题(1.1)标准有限元方法的最优L_2(2≤P<∞)估计.本文研究矩形剖分上的双k次有限元方法,用插值算子对近似解进行后处理,仅增加极少工作量,使整体收敛性提高一阶.本文证明了误差及任意阶时间导 进行后处理,仅增加极少工作量,使整体收敛性提高一阶.本文证明了误差及任意阶时间导数的H~1,W~(1,∞),L_p和L_∞的超收敛估计.若采用文[2]的预处理方法构造最优剖分,可将本文结果推广到一般区域(仍超收敛1/2阶).这样,采用低次有限元可获得高阶精度,从而大大节省了计算量.     

一类非线性椭圆方程的刘维尔型定理

设（Mⁿ,g）是一个n维非紧的完备黎曼流行.本文考虑有正解的非线性椭圆方程△_fu+au log u=0的刘维尔型定理,其中a是一个非零常数.利用Bochner公式和极大值原理,获得了以上方程在Bakry-Emery里奇曲率有下界时正解的Li-Yau型梯度估计和某些有关的刘维尔理论,推广了文献[7]的结果.     

中立型微分方程组连续线性多步法

我们曾对中立型微分方程组给出了任意阶的单步解法.但是,就计算量来说,多步法比较优越.本文将给出连续线性多步法,它类似于常微分方程组Adams线性多步法.当方程是常微且取离散解时,它就是Adams法;当方程不含导数时,它是某类Volterra泛函微分方程组的线性多步法(Volterra微分积分方程与迟延方程为其特例).本文的算法在     

A COMPARISON THEOREM FOR THE OSCILLATION OF DIFFERENTIAL EQUATIONS WITH ADVANCED ARGUMENT

ＡＣＯＭＰＡＲＩＳＯＮＴＨＥＯＲＥＭＦＯＲＴＨＥＯＳＣＩＬＬＡＴＩＯＮＯＦＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＡＤＶＡＮＣＥＤＡＲＧＵＭＥＮＴＬｉＹｏｎｇｋｕｎ（李永昆）（ＹｕｎｎａｎＵｎｉｖｅｒｓｉｔｙ，云南大学，邮编：６５００９１）...     

NOTES ON THE OSCILLATION FOR CERTAIN HYPERBOLIC EQUATIONS OF NEUTRAL TYPE

1IntroductionOwingtotheapplicationsinthefieldofnaturalscience,therehasbeenan.-.increasinginterestinoscillationtheoryofhyperbolicpartialfuncti0naldiffe-rentialequations['-']-Forexample,K.Kreith,T.KusonoandN.Yosidain[1],ChenandYuin[2]concernedthefollowingequations,respectivelyWen0tethatthoseworkshavebeenc0ncernedwith0nlythecase0fdiscretedeviatingarguments,theresultsoftheequationswithcontinu0usdeviatingargumentsareverylittle.Weknowonly0ntheworksofaclassof0rdinarydifferentialequations[5],parab…     

二阶拟线性混合（椭圆—双曲）型方程的Frankl问题

本文证明了一类二阶阶拟线性混合型方程Frankl边值问题解的唯一性与存在性,文中先给出解后一种表示式,据此证明边值问题解的唯一性,进而求得解的估计式,据此再使用复分析理论与“参数开拓法”证明了边值问题解的存在性,这里使用的方法有别于其他作者对混合型方程通常使用的积分方程方法。