可化约拟线性双曲组带一类非局部边界条件的精确边界能控性

先证明了一类非线性积分方程解的存在唯一性,利用此结果,建立了可化约拟线性双曲组带一类非局部边界条件的单侧精确边界能控性.     

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.     

一类拟线性双曲型方程组混合初-边值问题的半整体C1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-边值问题半整体C1解的存在唯一性.     

拟线性双曲型方程(组)的精确能控性

本文为作者在中国科学院数学与系统科学研究院举办的第六届华罗庚数学讲座上的讲稿.§1　引言——从常微分方程谈起考虑如下的线性常微分方程组dXdt=AX+Bu,(1.1)其中,t为自变量(时间),X=(X1,…,XN)为状态变量,u=(u1,…,um)为控制变量,而A及B分别为N×N及N×m常数阵.(1.1)是一个有限维的动力系统.说该系统在时间区间[0,T](T>0)上具有精确能控性,是指对于在t=0时任意给定的初值X0及在t=T时任意给定的终值XT,一定能找到[0,T]上的控制函数u=u(t),使Cauchy问题dXdt=AX+Bu(t),(1.2)t=0:X=X0(1.3)的解X=X(t)精确地满足终端条件t=T:X=X…     

一维绝热流方程组的精确边界能控性

利用一阶拟线性双曲组混合初边值问题的精确能控性理论,通过对边界速度或压强的控制,实现了一维绝热流方程组的精确边界能控性.     

双曲系统的节点状态的精确边界能控性

在此综述性文章中,我们将回顾关于节点状态的精确边界能控性的已有结果,并对此主题之进一步研究给出若干建议     

具耗散项拟线性双曲型方程组的边值问题

本文考虑具耗散项一阶拟线性双曲型方程组的具有自由边界的典型自由边值问题．在一些合理假设下,证明了其经典解的整体存在性定理．     

河渠非定常流的精确边界能控性

借助于一阶拟线性双曲型方程组混合初边值问题的半整体C^1解理论对单个河道及弦状网络河道中的非定常流动分别讨论了在闸门边界条件下的精确边界能控性问题,并对在泄洪边界条件下的精确边界能控性进行了相应的讨论。     

具非线性阻尼的拟线性双曲型方程

本文讨论了来自于神经传播和具粘性效应的杆的纵振动问题的一类具非线性阻尼的拟线性双曲型方程的初边值问题解的存在唯一性。所用的方法是能量估计和Ｐａｚｙ的半解方法。     

拟线性双曲组一类非局部混合初-边值问题的半整体C1解

在研究拟线性弦振动方程带第三类边值问题的精确边界能控性时,出现了拟线性双曲组一类非局部混合初-边值问题.论文先证明该类非局部混合问题局部C1解的存在惟一性,并考察其存在高度的性质,进而利用一致先验估计证明半整体C1解的存在惟一性,并以此为基础研究相应问题的精确边界能控性,最后为便于应用,将论文的结论写成了可化约方程组的情形.     

高阶拟线性双曲型方程的精确边界能控性

By means of the existence and uniqueness of semi-global C^1 solution to the mixed initial-boundary value problem with general nonlinear boundary conditions for first order quasilinear hyperbolic systems with zero eigenvalues ,the local exact boundary controllability for higher order quasilinear hyperbolic equations is established.     

Exact boundary observability for nonautonomous first-order quasilinear hyperbolic systems

By means of the theory on the semiglobal C¹ solution to the mixed initial-boundary value problem for first-order quasilinear hyperbolic systems, we establish the local exact boundary observability for general nonautonomous first-order quasilinear hyperbolic systems without zero eigenvalues and reveal the essential difference between nonautonomous hyperbolic systems and autonomous hyperbolic systems. Copyright © 2008 John Wiley & Sons, Ltd.     

Exact controllability of nodal profile for 1‐D first order quasilinear hyperbolic systems with internal controls

For 1‐D first order quasilinear hyperbolic systems without zero eigenvalues, based on the theory of exact boundary controllability of nodal profile, using an extension method, the exact controllability of nodal profile can be realized in a shorter time by means of additional internal controls acting on suitably small space‐time domains. On the other hand, using a perturbation method, the exact controllability of nodal profile for 1‐D first order quasilinear hyperbolic systems with zero eigenvalues can be realized by additional internal controls to the part of equations corresponding to zero eigenvalues. Furthermore, by adding suitable internal controls to all the equations on suitable domains, the exact controllability of nodal profile for systems with zero eigenvalues can be realized in a shorter time.     

Exact boundary controllability of nodal profile for quasilinear hyperbolic systems in a tree‐like network

In this paper, the exact boundary controllability of nodal profile is established for quasilinear hyperbolic systems with general nonlinear boundary and interface conditions in a tree‐like network with general topology. The basic principles for giving nodal profiles and for choosing boundary controls are presented, respectively. Copyright © 2011 John Wiley & Sons, Ltd.     

Exact boundary controllability for a kind of second‐order quasilinear hyperbolic systems and its applications

In this paper, by means of a constructive method based on the existence and uniqueness of the semi‐global C² solution, we establish the local exact boundary controllability for a kind of second‐order quasilinear hyperbolic systems. As an application, we obtain the one‐sided local exact boundary controllability for the first‐order quasilinear hyperbolic systems of diagonal form with boundary conditions in which the diagonal variables corresponding to the positive eigenvalues and those corresponding to the negative eigenvalues are decoupled. Copyright © 2009 John Wiley & Sons, Ltd.     

Exact boundary controllability for non‐autonomous quasilinear wave equations

In this paper, we first show that quite different from the autonomous case, the exact boundary controllability for non‐autonomous wave equations possesses various possibilities. Then we adopt a constructive method to establish the exact boundary controllability for one‐dimensional non‐autonomous quasilinear wave equations with various types of boundary conditions. Finally, we apply the results to multi‐dimensional quasilinear wave equation with rotation invariance. Copyright © 2007 John Wiley & Sons, Ltd.     

Initial boundary value problems for quasilinear symmetric hyperbolic systems with characteristic boundary

This paper is devoted to initial boundary value problems for quasi-linear symmetric hyperbolic systems in a domain with characteristic boundary. It extends the theory on linear symmetric hyperbolic systems established by Friedrichs to the nonlinear case. The concept on regular characteristics and dissipative boundary conditions are given for quasilinear hyperbolic systems. Under some assumptions, an existence theorem for such initial boundary value problems is obtained. The theorem can also be applied to the Euler system of compressible flow. __________ Translated from Chinese Annals of Mathematics, Ser. A, 1982, 3(2): 223–232     

Exact controllability for 1‐D quasilinear wave equations with internal controls

For 1‐D quasilinear wave equations with different types of boundary conditions, based on the theory of the local exact boundary controllability, using an extension method, the author establishes the exact controllability in a shorter time by means of internal controls acting on suitable domains. In particular, the exact controllability can be realized only by internal controls, and the control time can be arbitrarily small. Copyright © 2016 John Wiley & Sons, Ltd.     

Exact boundary observability for a kind of second order quasilinear hyperbolic systems and its applications

In this paper, by means of a constructive method based on the existence and uniqueness of the semi-global C² solution, we establish the local exact boundary observability for a kind of second order quasilinear hyperbolic systems. As an application, we obtain the one-sided local exact boundary observability for a kind of first order quasilinear hyperbolic systems of diagonal form with boundary conditions in which the diagonal variables corresponding to the positive eigenvalues and those corresponding to the negative eigenvalues are decoupled.