Frontiers of Mathematics in China >

2020 , Vol. 15 >Issue 4: 727 - 748

DOI: https://doi.org/10.1007/s11464-020-0848-7

RESEARCH ARTICLE

Partial approximate boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls

  • Chenmu WANG ,
  • Yanyan WANG
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  • School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received date: 09 Feb 2020

Accepted date: 23 Jun 2020

Published date: 15 Aug 2020

Copyright

2020 Higher Education Press
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Abstract

In this paper, we propose the concept of partial approximate boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls, and make a deep discussion on it. We analyze the relation-ship between the partial approximate boundary synchronization and the partial exact boundary synchronization, and obtain sufficient conditions to realize the partial approximate boundary synchronization and necessary conditions of Kalman's criterion. In addition, with the help of partial synchronization decomposition, a condition that the approximately synchronizable state does not depend on the sequence of boundary controls is also given.

Key words： Coupled system of wave equations; partial approximate boundary synchronization; partially approximately synchronizable state

Cite this article

Chenmu WANG , Yanyan WANG . Partial approximate boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls[J]. Frontiers of Mathematics in China, 2020 , 15(4) : 727 -748 . DOI: 10.1007/s11464-020-0848-7

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