This paper deals with the solutions of time independent Schrodinger wave equation for a two-dimensional PT-symmetric coupled quintic potential in its most general form. Employing wavefunction ansatz method, general an...This paper deals with the solutions of time independent Schrodinger wave equation for a two-dimensional PT-symmetric coupled quintic potential in its most general form. Employing wavefunction ansatz method, general analytic expressions for eigenvalues and eigenfunctions for first four states are obtained. Solutions of a particular case are also presented.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
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 bound...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.展开更多
In this paper, an interconnected wave-ODE system with K-V damping in the wave equation and unknown parameters in the ODE is considered. It is found that the spectrum of the system operator is composed of two parts： P...In this paper, an interconnected wave-ODE system with K-V damping in the wave equation and unknown parameters in the ODE is considered. It is found that the spectrum of the system operator is composed of two parts： Point spectrum and continuous spectrum. The continuous spectrum consists of an isolated point 1 1/d, and there are two branches of the asymptotic eigenvalues： The first branch is accumulating towards 1 -2, and the other branch tends to -∞. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. As a consequence, the spectrum-determined growth condition and exponential stability of the system are concluded.展开更多
文摘This paper deals with the solutions of time independent Schrodinger wave equation for a two-dimensional PT-symmetric coupled quintic potential in its most general form. Employing wavefunction ansatz method, general analytic expressions for eigenvalues and eigenfunctions for first four states are obtained. Solutions of a particular case are also presented.
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.
文摘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.
基金supported by Shanxi Youth Foundation under Grant No.2013021002-1the National Natural Science Foundation of China under Grant Nos.61074049 and 61273130
文摘In this paper, an interconnected wave-ODE system with K-V damping in the wave equation and unknown parameters in the ODE is considered. It is found that the spectrum of the system operator is composed of two parts： Point spectrum and continuous spectrum. The continuous spectrum consists of an isolated point 1 1/d, and there are two branches of the asymptotic eigenvalues： The first branch is accumulating towards 1 -2, and the other branch tends to -∞. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. As a consequence, the spectrum-determined growth condition and exponential stability of the system are concluded.
