Exact Controllability of Wave Equations with Interior Degeneracy and One-Sided Boundary Control  

作　　者：BAI Jinyan CHAI Shugen 

机构地区：[1]School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China [2]School of Mathematics,Jinzhong University,Taiyuan 030006,China

出　　处：《Journal of Systems Science & Complexity》2023年第2期656-671,共16页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant No.12271316;the National Natural Science Foundation of China for the Youth under Grant No.11801339;Shanxi Sciences Project for Selected Overseas Scholars under Grant No.2018–172;the Technical Innovation Team of Jinzhong University under Grant No.202111。

摘　　要：In this paper,the authors mainly consider the exact controllability for degenerate wave equation,which degenerates at the interior point,and boundary controls acting at only one of the boundary points.The main results are that,it is possible to control both the position and the velocity at every point of the body and at a certain time T for the wave equation with interior weakly degeneracy.Moreover,it is shown that the exact controllability fails for the wave equation with interior strongly degeneracy.In order to steer the system to a certain state,one needs controls to act on both boundary points for the wave equation with interior strongly degeneracy.The difficulties are addressed by means of spectral analysis.

关 键 词：Boundary control degenerate wave equation exact controllability interior degeneracy 

分 类 号：O175[理学—数学]