共查询到20条相似文献,搜索用时 31 毫秒
1.
Ke WANG 《Frontiers of Mathematics in China》2011,6(3):545-555
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
2.
Zhiqiang Wang 《Mathematical Methods in the Applied Sciences》2007,30(11):1311-1327
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
3.
Tatsien Li 《Mathematical Methods in the Applied Sciences》2006,29(13):1543-1553
By means of a direct and constructive method based on the theory of semi‐global C2 solution, the local exact boundary observability and an implicit duality between the exact boundary controllability and the exact boundary observability are shown for 1‐D quasilinear wave equations with various boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
4.
Exact boundary controllability for 1‐D quasilinear wave equations with dynamical boundary conditions
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Yue Wang Günter Leugering Tatsien Li 《Mathematical Methods in the Applied Sciences》2017,40(10):3808-3820
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
5.
Kaili Zhuang 《Mathematical Methods in the Applied Sciences》2016,39(18):5162-5174
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
6.
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
7.
Exact controllability of nodal profile for 1‐D first order quasilinear hyperbolic systems with internal controls
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Kaili Zhuang 《Mathematical Methods in the Applied Sciences》2017,40(18):6565-6580
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
8.
Lixin Yu 《Mathematical Methods in the Applied Sciences》2010,33(3):273-286
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
9.
Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the authors apply a unified constructive method to establish the local exact boundary(null) controllability and the local boundary(weak) observability for a coupled system of 1-D quasilinear wave equations with various types of boundary conditions. 相似文献
10.
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
YuLixin 《高校应用数学学报(英文版)》2005,20(2):127-141
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
11.
In this paper, we consider the asymptotic stability of the exact boundary controllability of nodal profile for 1D quasi-linear wave equations. First, for 1D quasi-linear hyperbolic systems with zero eigenvalues, we establish the existence and uniqueness of semiglobal classical solution to the one-sided mixed initial-boundary value problem on a semibounded initial axis and discuss the asymptotic behavior of the corresponding solutions under different hypotheses on the initial data. Based on these results, we obtain the asymptotic stability of the exact boundary controllability of nodal profile for 1D quasi-linear wave equations on a semibounded time interval. 相似文献
12.
Li Tatsien 《Mathematical Methods in the Applied Sciences》2004,27(9):1089-1114
In this paper we establish the exact boundary controllability for quasilinear hyperbolic systems with interface conditions. As an application, we get the exact boundary controllability of unsteady flows in a string‐like network of open canals. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
13.
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
14.
Qilong Gu Tatsien Li 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009,26(6):2373-2384
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
15.
Tatsien Li 《Mathematische Nachrichten》2005,278(3):278-289
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
16.
Ke WANG 《数学年刊B辑(英文版)》2011,32(6):803-822
Based on the theory of semi-global C
1 solution and the local exact boundary controllability for first-order quasilinear hyperbolic systems, the local exact boundary
controllability for a kind of second-order quasilinear hyperbolic systems is obtained by a constructive method. 相似文献
17.
Strong (Weak) Exact Controllability and Strong (Weak) Exact Observability for Quasilinear Hyperbolic Systems 总被引:3,自引:2,他引:1
Numerical approximations of Cahn-Hilliard phase-field model for the two-phase incompressible flows are considered in this paper.Several efficient and energy stable time discretization schemes for the coupled nonlinear Cahn-Hilliard phase-field system for both the matched density case and the variable density case are constructed,and are shown to satisfy discrete energy laws which are analogous to the continuous energy laws. 相似文献
18.
For general first-order quasilinear hyperbolic systems, based on the
analysis of simple wave solutions along characteristic trajectories,
the global two-sided exact boundary controllability is achieved in a
relatively short controlling time. 相似文献
19.
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. 相似文献
20.
Controllability of classical solutions implies controllability of weak solutions for a coupled system of wave equations and its application
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Xing Lu 《Mathematical Methods in the Applied Sciences》2016,39(4):709-721
In this paper, for a coupled system of one‐dimensional wave equations with Dirichlet boundary controls, we show that the controllability of classical solutions implies the controllability of weak solutions. This conclusion can be applied in proving some results that are hardly obtained by a direct way in the framework of classical solutions. For instance, we strictly derive the necessary conditions for the exact boundary synchronization by two groups in the framework of classical solutions for the coupled system of wave equations. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献