For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an appl...For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an application, the authors show the local exact boundary controllability for a kind of nonlinear vibrating string problem.展开更多
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 couple...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.展开更多
The paper deals with the controllability of a heat equation. It is well-known that the heat equation yt - △y = uxE in （0, T） × Ω with homogeneous Dirichlet boundary conditions is null controllable for any T ...The paper deals with the controllability of a heat equation. It is well-known that the heat equation yt - △y = uxE in （0, T） × Ω with homogeneous Dirichlet boundary conditions is null controllable for any T 〉 0 and any open nonempty subset E of Ω. In this note, the author studies the case that E is an arbitrary measurable set with positive measure.展开更多
This paper proves the local exact one-sided boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws with characteristics with constant multiplicity. This generalizes th...This paper proves the local exact one-sided boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws with characteristics with constant multiplicity. This generalizes the results in [Li, T. and Yu, L., One-sided exact boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws, To appear in Journal de Mathematiques Pures et Appliquees, 2016.] for a class of strictly hyperbolic systems of conservation laws.展开更多
基金Project supported by the Special Funds forMajor State Basic Research Projects ofChina.
文摘For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an application, the authors show the local exact boundary controllability for a kind of nonlinear vibrating string problem.
文摘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.
基金supported by the National Natural Science Foundation of China (No. 10671040)the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 200522) the Program for the New Century Excellent Talents in University of China (No. 06-0359)
文摘The paper deals with the controllability of a heat equation. It is well-known that the heat equation yt - △y = uxE in （0, T） × Ω with homogeneous Dirichlet boundary conditions is null controllable for any T 〉 0 and any open nonempty subset E of Ω. In this note, the author studies the case that E is an arbitrary measurable set with positive measure.
基金supported by the National Natural Science Foundation of China(No.11501122)
文摘This paper proves the local exact one-sided boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws with characteristics with constant multiplicity. This generalizes the results in [Li, T. and Yu, L., One-sided exact boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws, To appear in Journal de Mathematiques Pures et Appliquees, 2016.] for a class of strictly hyperbolic systems of conservation laws.
