Exact synchronization by groups for a coupled system of wave equations with Dirichlet boundary controls

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• 作者：Tatsien Li^a ; ^b ; ^{dqli@fudan.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Bopeng Rao^c ; ^{bopeng.rao@math.unistra.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：93B05 ; 93B07 ; 93C20
• 刊名：Journal de mathematiques pures et appliquees
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：105
• 期：1
• 页码：86-101
• 全文大小：380 K

文摘

In this paper, we show both the necessity and the sufficiency of the compatibility condition on the coupling matrix for the exact synchronization by groups for a coupled system of wave equations with Dirichlet boundary controls. Moreover, if the coupling matrix is diagonalizable by blocks in a suitable basis, for example, as in the cases for a symmetric matrix, the state of synchronization by groups can be uniquely determined independently of the applied boundary controls. In the general case, the state of synchronization by groups depends on the boundary controls; however, we give an estimate of the difference between the state of synchronization by groups and the solution to a problem independent of boundary controls.