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
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
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
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
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.
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.
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.
