Nonlinear boundary feedback control to a Timoshenko beam is studied. Under some nonlinear boundary feedback controls, the nonlinear semi group theory is used to show the well posedness for the correspnding closed loop...Nonlinear boundary feedback control to a Timoshenko beam is studied. Under some nonlinear boundary feedback controls, the nonlinear semi group theory is used to show the well posedness for the correspnding closed loop system. Then by using the energy perturbed method, it is proved that the vibration of the beam under the proposed control actions decays asymptotically or exponentially as t →∞.展开更多
In this paper, we consider a system of coupled quasilinear viscoelastic equa- tions with nonlinear damping. We use the perturbed energy method to show the general decay rate estimates of energy of solutions, which ext...In this paper, we consider a system of coupled quasilinear viscoelastic equa- tions with nonlinear damping. We use the perturbed energy method to show the general decay rate estimates of energy of solutions, which extends some existing results concerning a general decay for a single equation to the case of system, and a nonlinear system of viscoelastic wave equations to a quasilinear system.展开更多
In this paper, the stabilization problem of Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory and energy-perturbed method, it is shown that the vibrati...In this paper, the stabilization problem of Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory and energy-perturbed method, it is shown that the vibration of the beam under the proposed control action decays exponentially or in negative power of time t as t - ∞.展开更多
Abstract In this paper, the stabilization problem of nonuniform Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory, energy-perturbed approach and expone...Abstract In this paper, the stabilization problem of nonuniform Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory, energy-perturbed approach and exponential multiplier method, it is shown that the vibration of the beam under the proposed control action decays exponentially or in negative power of time t as t M X.展开更多
文摘Nonlinear boundary feedback control to a Timoshenko beam is studied. Under some nonlinear boundary feedback controls, the nonlinear semi group theory is used to show the well posedness for the correspnding closed loop system. Then by using the energy perturbed method, it is proved that the vibration of the beam under the proposed control actions decays asymptotically or exponentially as t →∞.
基金supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education,Science and Technology (2011-0007870)
文摘In this paper, we consider a system of coupled quasilinear viscoelastic equa- tions with nonlinear damping. We use the perturbed energy method to show the general decay rate estimates of energy of solutions, which extends some existing results concerning a general decay for a single equation to the case of system, and a nonlinear system of viscoelastic wave equations to a quasilinear system.
文摘In this paper, the stabilization problem of Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory and energy-perturbed method, it is shown that the vibration of the beam under the proposed control action decays exponentially or in negative power of time t as t - ∞.
基金Supported by the National Natural Science Foundation of China (Grant No.60174008).
文摘Abstract In this paper, the stabilization problem of nonuniform Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory, energy-perturbed approach and exponential multiplier method, it is shown that the vibration of the beam under the proposed control action decays exponentially or in negative power of time t as t M X.
基金国家自然科学基金(12071413,11971487)the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie(823731CONMECH)+5 种基金长沙理工大学数学模型与分析重点实验室项目(2018MMAEZD05)湖南省教育厅科学研究项目(18A325)广西自科基金(2018GXNSFDA138002)湖南自科基金(2021JJ30297,2020JJ2038)湖南理工学院科研创新团队项目(2019-TD-15)海南省计算与应用重点实验室开放基金(JSKX201905)。
