EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH ZERO EIGENVALUES＊＊＊

For a class of mixed initial-boundary value problem for general quasilinear hyperbolic sys-tems with zero eigenvalues, the authors establish the local exact controllability with boundary controls acting on one end or on two ends and internai controls acting on a part of equations in the system.     

EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH VERTICAL CHARACTERISTICS

We consider first order quasilinear hyperbolic systems with vertical characteristics. It was shown in [4] that such systems can be exactly controllable with the help of internal controls applied to the equations corresponding to zero eigenvalues. However, it is possible that, for physical or engineering reasons, we can not put any control on the equations corresponding to zero eigenvalues. In this paper, we will establish the exact controllability only by means of physically meaningfnl internal controls applied to the equations corresponding to non-zero eigenvalues. We also show the exact controllability for a very simplified model by means of switching controls.     

COMPLETE REDUCIBILITY FOR QUASILINEAR HYPERBOLIC SYSTEMS

In this paper we present a necessary and sufficient condition to guarantee the complete reducibility for quasilinear hyperbolic systems and give some examples.     

一类边界控制半线性抛物型系统的逼近能控性

本文考虑一类Ｄｉｒｉｃｈｌｅｔ型边界控制半线性抛物型系统，应用半群理论和非线性分析的方法，证明了系统解映射的连续性，给出了系统逼近能控的一个充分条件．对于Ｎｅｕｍａｎｎ型边界控制或混合型边界控制的半线性抛物型系统，可以得到类似的结果．     

高维拟线性双曲型方程组的对角化问题

本文讨论了高维一阶拟线性方程组可对角化的条件，并给出其在二维等熵流方程组、三维空气动力学方程组及具有旋转对称性的守恒律组等情形的应用；然后给出了高维拟线性对角型方程组Ｃａｕｃｈｙ问题存在整体经典解的一个充要条件，并给出其应用。     

BREAKDOWN OF CLASSICAL SOLUTION TO A KIND OF QUASILINEAR NON-STRICTLY HYPERBOLIC SYSTEMS

In this article, the author considers the Cauchy problem for quasilinear non-strictly hyperbolic systems and obtain a blow-up result for the C¹ solution to the Cauchy problem with weaker decaying initial data.     

FORMATION OF SINGULARITIES FOR A KIND OF QUASILINEAR NON－STRICTLY HYPERBOLIC SYSTEM

The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.     

BREAKDOWN OF CLASSICAL SOLUTION TO A KIND OF QUASILINEAR NON-STRICTLY HYPERBOLIC SYSTEMS

In this article, the author considers the Cauchy problem for quasilinear non-strict ly hyperbolic systems and obtain a blow-up result for the C1 solution to the Cauchy problem with weaker decaying initial data.     

一类拟线性双曲型方程组混合初-边值问题的半整体C~1解

本文证明了具零特征且形式更广泛的一类拟线性双曲型方程组的具有一般非线性边界条件的混合初 一边值问题半整体C1解的存在唯一性.     

CONSTRUCTION OF SOLUTIONS TO M-D RIEMANN PROBLEMS FOR A 2*2 QUASILINEAR HYPERBOLIC SYSTEM

The author studies M-D Riemann problems for a quasilinear nonstrictly byperbolic system.The initial date are taken as three different constants in three sections divided by three rays starting from the origin.From each direction of these rays two waves coming from infinity are allowed.All possible local singularity structures are carefully studied and classified.Then based on such analysis,existence and global singularity structure of the solution are obtained under some assumptions.     

一类半线性双曲系统的状态观测问题

本文考虑一类半线性双曲系统的状态观测问题,给出了一个(求解)算法并证明了其在某种相当强的意义上的有效性.     

一类拟线性椭圆型方程很弱解的局部正则性

本文考虑一类拟线性椭圆型方程的很弱解．使用Hodge分解等工具，得到了其局部正则性，推广了[1]之结果。     

LIFE-SPAN OF CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS WITH SLOW DECAY INITIAL DATA LIFE-SPAN OF CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS WITH SLOW DECAY INITIAL DATA

1. IntroductionConsider the following quasilinear systeman on~ A(u)~ = 0, (1.1)ot oxwhere u ~ (ul,'' t u.)" is the unknown vector function of (t, x) and A(u) ~ (ail(u)) is ann x n matrix with suitably smooth elements ail(u) (i, j = 1,... ) n).Suppose that the system (1.1) is strictly hyperbolic in a neighbourhood of u = 0, namely,for any given u in this domain, A(u) has n distinct real eigenvalues Al(u), AZ(u),'' j A.(u)such thatAl(u) < AZ(u) <'' < A.(u). (1.2)For i = 1,'',nl let h(u…     

以局部有限测度为初值的拟线性退化双曲方程BV解的存在唯一性

本文讨论了下列拟线性退化双曲方程ut (?)(u)x=0,以σ-有限的Borel测度为初值条件的Cauchy问题解的存在唯一性,其中在R上是连续的非减的函数.     

二阶拟线性微分方程组边值问题的三个对称正解

本文讨论二阶拟线性微分方程组边值问题( p(x'))'+a(t),(t,x,y)=0,( q(y'))'+b(t)g(t,x,y)=0,x(0)-B0(x'(0))=x(1)+Bo(x'(1))=0,y(0)-B1(y'(0))=y(1)+B1(y'(1))=0,其中f,g是非负连续的函数.利用五个泛函的不动点定理,赋予f和g一些增长条件保证至少三个对称正解的存在性.     

GLOBAL CLASSICAL SOLUTIONS WITH SMALL INITIAL TOTAL VARIATION FOR QUASILINEAR HYPERBOLIC SYSTEMS

By means of the continuous Glimm functional,a proof is given on the global existence ofclassical solutions to Cauchy problem for general first order quasilinear hyperbolic systems withsmall initial total rariation.     

一类带阻尼项的拟线性双曲型方程

本文讨论了从细杆的振动中提出的一类带阻尼项的拟线性双曲型方程的初边值问题的解在唯一性，利用已有的线性结果及动点定理结合能量估计建立了解的存在唯一性。     

CONTROLLABILITY AND OBSERVABILITY FOR A CLASS OF FRACTIONAL-ORDER IMPULSIVE SYSTEMS

This paper studies the controllability and observability for a class of fractionalorder impulsive systems.First,the basic acknowledgement of fractional-order systems is presented.Then the solution of the fractional-order impulsive systems is given.Finally,necessary and sufficient criteria for controllability and observability are obtained.     

LIFE-SPAN OF CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS WITH SLOWDECAY INITIAL DATA

The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with “slow” decay initial data. By constructing an example, first it is illustrated that the classical solution to this kind of Cauchy problem may blow up in a finite time, even if the system is weakly linearly degenerate. Then some lower bounds of the life-span of classical solutions are given in the case that the system is weakly linearly degenerate. These estimates imply that, when the system is weakly linearly degenerate, the classical solution exists almost globally in time. Finally, it is proved that Theorems 1.1-1.3 in [2] are still valid for this kind of initial data.