Equivalence between the internal observability and equation

作     者：LIU Wen-jun TU Zhi-yu LIU Wen-jun;TU Zhi-yu

作者机构：School of Mathematics and StatisticsNanjing University of Information Science and TechnologyNanjing 210044China 

出 版 物：《Applied Mathematics(A Journal of Chinese Universities)》 (高校应用数学学报（英文版）（B辑）)

年 卷 期：2024年第39卷第1期

页      面：89-97页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(11771216) the Key Research and Development Program of Jiangsu Province(Social Development)(BE2019725) the Qing Lan Project of Jiangsu Province。 

主　　题：Moore-Gibson-Thompson equation internal observability exponential stability 

摘      要：This paper is concerned with a third order in time linear Moore-Gibson-Thompson equation which describes the acoustic velocity potential in ultrasound wave program.Influenced by the work of Kaltenbacher,Lasiecka and Marchand(Control Cybernet.2011,40:971-988),we establish an observability inequality of the conservative problem,and then discuss the equivalence between the exponential stabilization of a dissipative system and the internal observational inequality of the corresponding conservative system.