In this paper, we study on the initial-boundary value problem for nonlinear wave equations of higher-order Kirchhoff type with Strong Dissipation: . At first, we prove the existence and uniqueness of the local solutio...In this paper, we study on the initial-boundary value problem for nonlinear wave equations of higher-order Kirchhoff type with Strong Dissipation: . At first, we prove the existence and uniqueness of the local solution by the Banach contraction mapping principle. Then, by “Concavity” method we establish three blow-up results for certain solutions in the case 1): , in the case 2): and in the case 3): . At last, we consider that the estimation of the upper bounds of the blow-up time is given for deferent initial energy.展开更多
The paper is concerned with the long-time behaviour of the travelling fronts of the damped wave equation αutt ＋ut = uxx -V′（u） on R. The long-time asymptotics of the solutions of this equation are quite similar t...The paper is concerned with the long-time behaviour of the travelling fronts of the damped wave equation αutt ＋ut = uxx -V′（u） on R. The long-time asymptotics of the solutions of this equation are quite similar to those of the corresponding reaction-diffusion equation ut = uxx - V′（u）. Whereas a lot is known about the local stability of travelling fronts in parabolic systems, for the hyperbolic equations it is only briefly discussed when the potential V is of bistable type. However, for the combustion or monostable type of V, the problem is much more complicated. In this paper, a local stability result for travelling fronts of this equation with combustion type of nonlinearity is established. And then, the result is extended to the damped wave equation with a case of monostable pushed front.展开更多
We investigate entanglement of assistance without and with decoherence using a local non-Hermitian operation, i.e.,parity–time(PT) symmetric operation. First we give the explicit expressions of entanglement of assist...We investigate entanglement of assistance without and with decoherence using a local non-Hermitian operation, i.e.,parity–time(PT) symmetric operation. First we give the explicit expressions of entanglement of assistance for a general W-like state of a three-qubit system under a local parity–time symmetric operation. Then for a famous W state without decoherence, we find that entanglement of assistance shared by two parties can be obviously enhanced with the assistance of the third party by a local parity–time symmetric operation. For the decoherence case, we provide two schemes to show the effects of local parity–time symmetric operation on improvement of entanglement of assistance against amplitude damping noise. We find that for the larger amplitude damping case the scheme of PT symmetric operation performed on one of two parties with the influence of noise is superior to that of PT symmetric operation performed on the third party without the influence of noise in suppressing amplitude damping noise. However, for the smaller amplitude damping case the opposite result is given. The obtained results imply that the local PT symmetric operation method may have potential applications in quantum decoherence control.展开更多
采用局部均值分解(Local Mean Decomposition,LMD)方法来识别机械系统固有频率和阻尼比。局部均值分解(LMD)方法可以自适应地将一个复杂信号分解为若干个具有一定物理意义的PF(Production Function)分量之和,采用LMD方法对脉冲激励下机...采用局部均值分解(Local Mean Decomposition,LMD)方法来识别机械系统固有频率和阻尼比。局部均值分解(LMD)方法可以自适应地将一个复杂信号分解为若干个具有一定物理意义的PF(Production Function)分量之和,采用LMD方法对脉冲激励下机械系统的加速度响应信号进行分解,得到一列具有物理意义的PF分量,每一个PF分量可以对应于某一个模态下的振动响应,进而就可以通过拟合瞬时频率和瞬时幅值曲线识别模态固有频率和阻尼比。先采用仿真信号进行了分析,使用LMD方法和经验模态分解方法(Empirical Mode Decomposition,EMD)对梁的瞬态响应实验数据进行模态识别并同仿真结果进行对比研究,结果表明用LMD进行模态分析具有较好的效果。展开更多
文摘In this paper, we study on the initial-boundary value problem for nonlinear wave equations of higher-order Kirchhoff type with Strong Dissipation: . At first, we prove the existence and uniqueness of the local solution by the Banach contraction mapping principle. Then, by “Concavity” method we establish three blow-up results for certain solutions in the case 1): , in the case 2): and in the case 3): . At last, we consider that the estimation of the upper bounds of the blow-up time is given for deferent initial energy.
文摘The paper is concerned with the long-time behaviour of the travelling fronts of the damped wave equation αutt ＋ut = uxx -V′（u） on R. The long-time asymptotics of the solutions of this equation are quite similar to those of the corresponding reaction-diffusion equation ut = uxx - V′（u）. Whereas a lot is known about the local stability of travelling fronts in parabolic systems, for the hyperbolic equations it is only briefly discussed when the potential V is of bistable type. However, for the combustion or monostable type of V, the problem is much more complicated. In this paper, a local stability result for travelling fronts of this equation with combustion type of nonlinearity is established. And then, the result is extended to the damped wave equation with a case of monostable pushed front.
基金Project supported by China Postdoctoral Science Foundation(Grant No.2017M622582)the Natural Science Foundation of Hunan Province of China(Grant No.2015JJ3092)+2 种基金the Research Foundation of Education Bureau of Hunan Province of China(Grant No.16B177)Applied Characteristic Disciplines in Hunan Province-Electronic Science and Technology of ChinaHunan-Provincial Key Laboratory of Photoelectric Information Integration and Optical Manufacturing Technology
文摘We investigate entanglement of assistance without and with decoherence using a local non-Hermitian operation, i.e.,parity–time(PT) symmetric operation. First we give the explicit expressions of entanglement of assistance for a general W-like state of a three-qubit system under a local parity–time symmetric operation. Then for a famous W state without decoherence, we find that entanglement of assistance shared by two parties can be obviously enhanced with the assistance of the third party by a local parity–time symmetric operation. For the decoherence case, we provide two schemes to show the effects of local parity–time symmetric operation on improvement of entanglement of assistance against amplitude damping noise. We find that for the larger amplitude damping case the scheme of PT symmetric operation performed on one of two parties with the influence of noise is superior to that of PT symmetric operation performed on the third party without the influence of noise in suppressing amplitude damping noise. However, for the smaller amplitude damping case the opposite result is given. The obtained results imply that the local PT symmetric operation method may have potential applications in quantum decoherence control.
