Exact controllability for quasilinear hyperbolic systems and its application to unsteady flows in a network of open canals

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.     

Exact Boundary Observability of Unsteady Supercritical Flows in a Tree-Like Network of Open Canals

The author establishes the exact boundary observability of unsteady supercritical flows in a tree-like network of open canals with general topology. An implicit duality between the exact boundary controllability and the exact boundary observability is also given for unsteady supercritical flows.     

Exact boundary controllability of unsteady supercritical flows in a tree‐like network of open canals

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.     

Boundary controllability for the semilinear Schrödinger equations on Riemannian manifolds

We study the boundary exact controllability for the semilinear Schrödinger equation defined on an open, bounded, connected set Ω of a complete, n-dimensional, Riemannian manifold M with metric g. We prove the locally exact controllability around the equilibria under some checkable geometrical conditions. Our results show that exact controllability is geometrical characters of a Riemannian metric, given by the coefficients and equilibria of the semilinear Schrödinger equation. We then establish the globally exact controllability in such a way that the state of the semilinear Schrödinger equation moves from an equilibrium in one location to an equilibrium in another location.     

Exact boundary controllability of nodal profile for 1-D quasilinear wave equations

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.     

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.     

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.     

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。     

Exact Boundary Controllability of Weak Solutions for a Kind of First Order Hyperbolic System — the HUM Method*

The exact boundary controllability and the exact boundary observability for the 1-D first order linear hyperbolic system were studied by the constructive method in the framework of weak solutions in the work [Lu, X. and Li, T. T., Exact boundary controllability of weak solutions for a kind of first order hyperbolic system — the constructive method, Chin. Ann. Math. Ser. B, 42(5), 2021, 643–676]. In this paper, in order to study these problems from the viewpoint of duality, the authors establish ...     

Exact Boundary Controllability for a Kind of Second-Order Quasilinear Hyperbolic Systems

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.     

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.     

LOCAL EXACT BOUNDARY CONTROLLABILITY FOR A CLASS OF QUASILINEAR HYPERBOLIC SYSTEMS

InroductionLet us consider the following irst order quaslllnear hyperbolic     

Some exact controllability results for the linear KdV equation and uniform controllability in the zero-dispersion limit

In this paper, we deal with controllability properties of linear and nonlinear Korteweg-de Vries equations in a bounded interval. The main part of this paper is a result of uniform controllability of a linear KdV equation in the limit of zero-dispersion. Moreover, we establish a result of null controllability for the linear equation via the left Dirichlet boundary condition, and of exact controllability via both Dirichlet boundary conditions. As a consequence, we obtain some local exact controllability results for the nonlinear KdV equation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Controllability of classical solutions implies controllability of weak solutions for a coupled system of wave equations and its application

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.     

A note on the exact synchronization by groups for a coupled system of wave equations

By means of a non‐exact controllability result, we show the necessity of the conditions of compatibility for the exact synchronization by two groups for a coupled system of wave equations with Dirichlet boundary controls. Copyright © 2013 John Wiley & Sons, Ltd.     

A note on the exact synchronization by groups for a coupled system of wave equations

By means of a non‐exact controllability result, we show the necessity of the conditions of compatibility for the exact synchronization by two groups for a coupled system of wave equations with Dirichlet boundary controls. Copyright © 2014 John Wiley & Sons, Ltd.     

One-sided exact boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws

In this paper, the one-sided exact boundary null controllability of entropy solutions is studied for a class of general strictly hyperbolic systems of conservation laws, whose negative (or positive) characteristic families are all linearly degenerate. The authors first prove the well-posedness of semi-global solutions constructed as the limit of ε-approximate front tracking solutions to the mixed initial-boundary value problem with general nonlinear boundary conditions and they establish various properties of both the ε-approximate front tracking solutions and such solutions. By means of essential modifications of the strategy suggested by the first author in [17] originally for the local exact boundary controllability in the framework of classical solutions, the one-sided local exact boundary null controllability of entropy solutions can then be realized via boundary controls acting on one side of the boundary, where the incoming characteristics are all linearly degenerate.     

Exact Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls

In this paper, the exact synchronization for a coupled system of wave equations with Dirichlet boundary controls and some related concepts are introduced. By means of the exact null controllability of a reduced coupled system, under certain conditions of compatibility, the exact synchronization, the exact synchronization by groups, and the exact null controllability and synchronization by groups are all realized by suitable boundary controls.     

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.     

Strong （Weak） Exact Controllability and Strong （Weak） Exact Observability for Quasilinear Hyperbolic Systems

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.