In this paper, we investigate the eigenvalue problem of forward-backward doubly stochastic dii^erential equations with boundary value conditions. We show that this problem can be represented as an eigenvalue problem o...In this paper, we investigate the eigenvalue problem of forward-backward doubly stochastic dii^erential equations with boundary value conditions. We show that this problem can be represented as an eigenvalue problem of a bounded continuous compact operator. Hence using the famous Hilbert-Schmidt spectrum theory, we can characterize the eigenvalues exactly.展开更多
In this paper the stability and control of complex dynamic system with elastic structure are investigated. As the dynamic model of the system is described by the coupled system of ordinary differential equations and p...In this paper the stability and control of complex dynamic system with elastic structure are investigated. As the dynamic model of the system is described by the coupled system of ordinary differential equations and partial differential equations, due to the effect of structure damping on the motion it is difficult to analyse the dynamic behavior of the system by the classical methods. By means of the spectrum and semigroup theories of operators in functional spaces, we have proved the existence and the uniqueness of the solution of the system. Choosing some control laws, the elastic vibrations, including the bending vibration and the torsional vibration, can be exponentially stable and the attitude orientation of the beam will be held.展开更多
基金The NSF (10601019 and J0630104) of ChinaChinese Postdoctoral Science Foundation and 985 Program of Jilin University.
文摘In this paper, we investigate the eigenvalue problem of forward-backward doubly stochastic dii^erential equations with boundary value conditions. We show that this problem can be represented as an eigenvalue problem of a bounded continuous compact operator. Hence using the famous Hilbert-Schmidt spectrum theory, we can characterize the eigenvalues exactly.
基金Project supported by the National Natural Science Foundation of China and Astronautics Ministry
文摘In this paper the stability and control of complex dynamic system with elastic structure are investigated. As the dynamic model of the system is described by the coupled system of ordinary differential equations and partial differential equations, due to the effect of structure damping on the motion it is difficult to analyse the dynamic behavior of the system by the classical methods. By means of the spectrum and semigroup theories of operators in functional spaces, we have proved the existence and the uniqueness of the solution of the system. Choosing some control laws, the elastic vibrations, including the bending vibration and the torsional vibration, can be exponentially stable and the attitude orientation of the beam will be held.
