工程数学学报
工程數學學報
공정수학학보
CHINESE JOURNAL OF ENGINEERING MATHEMATICS
2007年
6期
1109-1116
,共8页
Rayleigh梁%点反馈%观测不等式%多项式衰减估计
Rayleigh樑%點反饋%觀測不等式%多項式衰減估計
Rayleigh량%점반궤%관측불등식%다항식쇠감고계
Rayleigh beam%pointwise feedback%observability inequality%polynomial decay estimate
本文研究在某种边界条件下具有点反馈的Rayleigh梁的能量衰减估计.证明了梁的能量一致指数衰减是不可能发生的.在能量空问中,当梁的能量非一致衰减时,由初始条件得到了梁的能量多项式衰减估计.本文的方法是由相应无阻尼系统产生观测不等式和迹正则性结果得到的衰减估计.
本文研究在某種邊界條件下具有點反饋的Rayleigh樑的能量衰減估計.證明瞭樑的能量一緻指數衰減是不可能髮生的.在能量空問中,噹樑的能量非一緻衰減時,由初始條件得到瞭樑的能量多項式衰減估計.本文的方法是由相應無阻尼繫統產生觀測不等式和跡正則性結果得到的衰減估計.
본문연구재모충변계조건하구유점반궤적Rayleigh량적능량쇠감고계.증명료량적능량일치지수쇠감시불가능발생적.재능량공문중,당량적능량비일치쇠감시,유초시조건득도료량적능량다항식쇠감고계.본문적방법시유상응무조니계통산생관측불등식화적정칙성결과득도적쇠감고계.
In this paper, we study the energy decay estimate of the Rayleigh beam which is subject to a pointwise feedback with certain boundary conditions, we show that the uniform energy decay may not occur. In the case of nonuniform decay in the energy space, we derive explicit polynomial decay estimates valid for regular initial data. Our method consists of deducing the decay estimates from observability inequalities for associated undamped problem via sharp trace regularity results.
