Sharp Observability Inequalities for the 1-D Plate Equation with a Potential  

作　　者：Xiaoyu FU 

机构地区：[1]College of Mathematics,Sichuan University,Chengdu 610064,China [2]Department of Mathematics,Indian Institute of Technology,Bombay,Mumbai 400076,India

出　　处：《Chinese Annals of Mathematics,Series B》2012年第1期91-106,共16页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China (No. 10901114);the Doctoral Fund for New Teachers of the Ministry of Education of China (No. 20090181120084) ;the National Basic Research Program of China (No. 2011CB808002)

摘　　要：This paper deals with the problem of sharp observability inequality for the 1-D plate equation wtt ＋ wxxxx ＋ q（t, x）w = 0 with two types of boundary conditions w = wxx = 0 or w = wx = 0, and q（t, x） being a suitable potential. The author shows that 2 the sharp observability constant is of order exp（C｜｜q｜｜^2/7∞） for ｜｜q｜｜∞〉 1. The main tools to derive the desired observability inequalities are the global Carleman inequalities, based on a new point wise inequality for the fourth order plate operator.

关 键 词：Observability inequality Plate equation Point-wise estimate Carlemanestimate 

分 类 号：O178[理学—数学] O231[理学—基础数学]