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

作     者：Xiaoyu FU 

作者机构：College of MathematicsSichuan UniversityChengdu 610064China Department of MathematicsIndian Institute of TechnologyBombayMumbai 400076India 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2012年第33卷第1期

页      面：91-106页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 0701[理学-数学] 071101[理学-系统理论] 0811[工学-控制科学与工程] 070101[理学-基础数学] 

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) 

主　　题：Observability inequality Plate equation Point-wise estimate Carlemanestimate 

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.