具有内部点耗散的Timoshenko梁的能量衰减估计

ENERGY DECAY ESTIMATES OF TIMOSHENKO BEAM WITH A POINTWISE FEEDBACK FORCE

研究具有反馈控制力的Timoshenko梁的能量衰减．证明了梁的能量不是一致衰减的．当梁的能量不是一致衰减时,利用初始值的正则性和无阻尼问题的最佳正则性结果,给出了多项式衰减估计．

In this paper, we study the energy decay estimates of a Timoshenko beam which is subject to a pointwise control force. We show that uniform energy decay may not occur. We give explicit polynomial decay estimates valid for regular initial data, when nonuniform energy decay occurs. Our method consists of deducing the decay estimates from observability inequalities for the associated undamped problem via sharp trace regularity results.