Let H be a Hilbert space with the inner product and the induced norm（·,·） and ||·||respectively, and A a linear operator on H, and R=（-∞, ∞）. ρ（A）denotes the resolvent set of A and R（λ,A）, t...Let H be a Hilbert space with the inner product and the induced norm（·,·） and ||·||respectively, and A a linear operator on H, and R=（-∞, ∞）. ρ（A）denotes the resolvent set of A and R（λ,A）, the resolvent of A. As concerns the stabili-ty of C<sub>0</sub> semigroups, we have Theorem 1. Let T（t） be a C<sub>0</sub> semigroup on H with the infinitesimal generator A. ThenT（t）is exponentially stable if and only展开更多
We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the gener...We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the generators of ϕ<sup>j</sup>-bounded strongly continuous semigroups. Furthermore, these results are used to investigate the effect of the Perturbation on the type of the growth of sequences.展开更多
In this paper, we define the mild solution of the delay system, and consider the existence and uniqueness of the mild solution of the delay system. The relationship between the solution csf linear system and the one o...In this paper, we define the mild solution of the delay system, and consider the existence and uniqueness of the mild solution of the delay system. The relationship between the solution csf linear system and the one of the delay system will be considered. And we also discuss the exponential stability equivalence between the solution of the linear system and the mild solution of the delay system.展开更多
The stabilization of the Timoshenko equation of a nonuniform beam with locally distributed feedbacks is considered.It is proved that the system is exponentially stabilizable.The frequency domain method and the multipl...The stabilization of the Timoshenko equation of a nonuniform beam with locally distributed feedbacks is considered.It is proved that the system is exponentially stabilizable.The frequency domain method and the multiplier technique are applied.展开更多
In this paper,we consider a multi-state device redundant systems with common-cause failures and one standby unit. We proved C0-semigroup generated by the system operator is quasi-compact by analyzing its spectrum and ...In this paper,we consider a multi-state device redundant systems with common-cause failures and one standby unit. We proved C0-semigroup generated by the system operator is quasi-compact by analyzing its spectrum and estimating essential growth bound semi-group generated by this system, 0 is an isolated eigenvalue with algebra multiply one. Moreover, we prove it is also irreducible. So we obtain the time-dependent solution exponentially converges to the steady-state solution.展开更多
We consider a thermoelastic plate with dynamical boundary conditions. Using the contradictionargument of Pazy's well-known analyticity criterion and P.D.E. estimates, we prove that the corresponding C0semigroup is...We consider a thermoelastic plate with dynamical boundary conditions. Using the contradictionargument of Pazy's well-known analyticity criterion and P.D.E. estimates, we prove that the corresponding C0semigroup is analytic, hence exponentially stable.展开更多
The boundary stabilization problem of a Timoshenko beam attached with a mass at one end is studied. First, with linear boundary force feedback and moment control simultaneously at the end attached with the load, the e...The boundary stabilization problem of a Timoshenko beam attached with a mass at one end is studied. First, with linear boundary force feedback and moment control simultaneously at the end attached with the load, the energy corresponding to the closed loop system is proven to be exponentially convergent to zero as time t →∞. Then, some counterexamples are given to show that, in other casest the corresponding closed loop system is, in general, not stable asymtotically, let alone exponentially.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘Let H be a Hilbert space with the inner product and the induced norm（·,·） and ||·||respectively, and A a linear operator on H, and R=（-∞, ∞）. ρ（A）denotes the resolvent set of A and R（λ,A）, the resolvent of A. As concerns the stabili-ty of C<sub>0</sub> semigroups, we have Theorem 1. Let T（t） be a C<sub>0</sub> semigroup on H with the infinitesimal generator A. ThenT（t）is exponentially stable if and only
文摘We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the generators of ϕ<sup>j</sup>-bounded strongly continuous semigroups. Furthermore, these results are used to investigate the effect of the Perturbation on the type of the growth of sequences.
文摘In this paper, we define the mild solution of the delay system, and consider the existence and uniqueness of the mild solution of the delay system. The relationship between the solution csf linear system and the one of the delay system will be considered. And we also discuss the exponential stability equivalence between the solution of the linear system and the mild solution of the delay system.
基金Supported partially by the NSFC and the Science Foundation of China State Education Commission.
文摘The stabilization of the Timoshenko equation of a nonuniform beam with locally distributed feedbacks is considered.It is proved that the system is exponentially stabilizable.The frequency domain method and the multiplier technique are applied.
文摘In this paper,we consider a multi-state device redundant systems with common-cause failures and one standby unit. We proved C0-semigroup generated by the system operator is quasi-compact by analyzing its spectrum and estimating essential growth bound semi-group generated by this system, 0 is an isolated eigenvalue with algebra multiply one. Moreover, we prove it is also irreducible. So we obtain the time-dependent solution exponentially converges to the steady-state solution.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10071079).
文摘We consider a thermoelastic plate with dynamical boundary conditions. Using the contradictionargument of Pazy's well-known analyticity criterion and P.D.E. estimates, we prove that the corresponding C0semigroup is analytic, hence exponentially stable.
基金Project supported by the the National Key Project of China.
文摘The boundary stabilization problem of a Timoshenko beam attached with a mass at one end is studied. First, with linear boundary force feedback and moment control simultaneously at the end attached with the load, the energy corresponding to the closed loop system is proven to be exponentially convergent to zero as time t →∞. Then, some counterexamples are given to show that, in other casest the corresponding closed loop system is, in general, not stable asymtotically, let alone exponentially.
