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1.
By means of the general results on the exact boundary controllability for quasilinear hyperbolic systems, the author establishes the exact boundary controllability of unsteady flows in both a single open canal and a network of open canals with star configuration respectively. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

2.
In this paper we establish the exact boundary observability of unsteady flows in a tree‐like network of open canals with general topology. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

3.
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.  相似文献   

4.
5.
In this paper we establish the exact boundary controllability of unsteady supercritical flows in a tree‐like network of open canals with general topology. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

6.
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。  相似文献   

7.
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.  相似文献   

8.
高阶拟线性双曲型方程的精确边界能控性   总被引:1,自引:0,他引:1  
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.  相似文献   

9.
Based on the theory of semi‐global piecewise C2 solutions to 1D quasilinear wave equations, the local exact boundary controllability of nodal profile for quasilinear wave equations in a planar tree‐like network of strings with general topology is obtained by a constructive method. The principles of providing nodal profiles and of choosing and transferring boundary controls are presented, respectively. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

10.
Based on the theory of semi-global C 2 solution for 1-D quasilinear wave equations, the local exact boundary controllability of nodal profile for 1-D quasilinear wave equations is obtained by a constructive method, and the corresponding global exact boundary controllability of nodal profile is also obtained under certain additional hypotheses.  相似文献   

11.
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.  相似文献   

12.
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.  相似文献   

13.
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.  相似文献   

14.
By equivalently replacing the dynamical boundary condition by a kind of nonlocal boundary conditions, and noting a hidden regularity of solution on the boundary with a dynamical boundary condition, a constructive method with modular structure is used to get the local exact boundary controllability for 1‐D quasilinear wave equations with dynamical boundary conditions. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

15.
In this paper, by means of a constructive method based on the existence and uniqueness of the semi-global classical solution, we establish the local exact boundary observability for a kind of second-order quasilinear hyperbolic system in which the number of positive eigenvalues and the number of negative ones are not equal. As an application, we obtain the one-sided local exact boundary observability and two-sided local exact boundary observability with fewer observed values for 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 ones are decoupled.  相似文献   

16.
In this paper the local exact boundary controllability for quasilinear wave equations on a planar tree-like network of strings is established and the number of boundary controls is equal to the number of simple nodes minus 1.  相似文献   

17.
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.  相似文献   

18.
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.  相似文献   

19.
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  相似文献   

20.
In this paper, by means of a constructive method based on the theory of the existence and the uniqueness of the C1 solution to the Cauchy problem and the Goursat problem, the global exact boundary observability for the first‐order quasilinear hyperbolic systems of diagonal form with linearly degenerate characteristics is obtained. In the case that the system has no zero characteristics, we realize the two‐sided and one‐sided global exact boundary observability by the boundary observed values and obtain the observability inequality. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

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