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Induced generalized exact boundary synchronizations for a coupled system of wave equations

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Applied Mathematics(A Journal of Chinese Universities) 2020年第1期35卷 113-126页

作者： WANG Yan-yan School of Mathematical Sciences Fudan UniversityShanghai 200433China

Taking a coupled system of wave equations with Dirichlet boundary controls as an example,by splitting and merging some synchronization groups of the state variables cor-responding to a given generalized synchronization matrix,this paper introduces two kinds of induced generalized exact boundary synchronizations to better determine its generalized exactly synchronizable states.

关键词： coupled system of wave equations generalized exact boundary synchronization determination of generalized exactly synchronizable states

A Note on the Indirect Controls for a coupled system of wave equations

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Chinese Annals of Mathematics,Series B 2022年第3期43卷 359-372页

作者： Tatsien LI Bopeng RAO School of Mathematical Sciences Fudan UniversityShanghai 200433China Shanghai Key Laboratory for Contemporary Applied Mathematic Shanghai 200433China Nonlinear Mathematical Modeling and Methods Laboratory Shanghai 200433China Institut de Recherche Mathématique Avancée Universitéde Strasbourg67084 StrasbourgFrance

By a procedure of successive projections,the authors decompose a coupled system of wave equations into a sequence of ***,they can clarify the indirect controls and the total number of ***,the authors give a uniqueness... 详细信息

关键词： Indirect controls Approximate controllability coupled system of wave equations

Exact Internal Controllability and Synchronization for a coupled system of wave equations

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Chinese Annals of Mathematics,Series B 2023年第5期44卷 641-662页

作者： Chengxia ZU Tatsien LI Bopeng RAO School of Mathematics Hohai UniversityNanjing 211100China School of Mathematical Sciences Fudan UniversityShanghai 200433China Shanghai Key Laboratory for Contemporary Applied Mathematics/Nonlinear Mathematical Modelingand Methods Laboratory Shanghai 200433China Institut de Recherche Mathematique Avancee Universite de Strasbourg67084 StrasbourgFrance

In this paper the exact internal controllability for a coupled system of wave equations with arbitrarily given coupling matrix is *** on this result,the exact internal synchronization and the exact internal synchroniz... 详细信息

关键词： Exact internal controllability Exact internal synchronization by groups coupled system of wave equations

Generalized Exact Boundary Synchronization for a coupled system of wave equations with Dirichlet Boundary Controls

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Chinese Annals of Mathematics,Series B 2020年第4期41卷 511-530页

作者： Yanyan WANG School of Mathematical Sciences Fudan UniversityShanghai 200433China

This paper deals with the generalized exact boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls in the framework of weak solutions.A necessary and sufficient condition for the generalized exact boundary synchronization is obtained,and some results for its generalized exactly synchronizable states are given.

关键词： Generalized exact boundary synchronization coupled system of wave equations Generalized exactly synchronizable state Dirichlet boundary control

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

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Frontiers of Mathematics in China 2020年第4期15卷 727-748页

作者： Chenmu WANG Yanyan WANG School of Mathematical Sciences Fudan UniversityShanghai 200433China

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 *** analyze the relationship 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 *** 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.

关键词： coupled system of wave equations partial approximate boundary synchronization partially approximately synchronizable state

Exact Boundary Synchronization by Groups for a Kind of system of wave equations coupled with Velocities

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Chinese Annals of Mathematics,Series B 2023年第1期44卷 17-34页

作者： Xing LU Tatsien LI School of Mathematics Southeast UniversityNanjing 211189China School of Mathematical Sciences Fudan UniversityShanghai 200433China Shanghai Key Laboratory for Contemporary Applied Mathematic Fudan UniversityShanghai 200433China Nonlinear Mathematical Modeling and Methods Laboratory Fudan UniversityShanghai 200433China

This paper deals with the exact boundary controllability and the exact boundary synchronization for a 1-D system of wave equations coupled with *** problems can not be solved directly by the usual HUM method for wave equations,however,by transforming the system into a first order hyperbolic system,the HUM method for 1-D first order hyperbolic systems,established by Li-Lu(2022)and Lu-Li(2022),can be applied to get the corresponding results.

关键词： Exact boundary controllability Exact boundary synchronization coupled system of wave equations HUM method

On the Synchronizable system

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Chinese Annals of Mathematics,Series B 2020年第6期41卷 821-828页

作者： Zhen LEI Tatsien LI Bopeng RAO School of Mathematical Sciences Fudan UniversityShanghai 200433China Shanghai Key Laboratory for Contemporary Applied Mathematics Nonlinear Mathematical Modeling and Methods Laboratory Institut de Recherche Mathematique Avancee Universite de Strasbourg67084 StrasbourgFrance

In this paper,the synchronizable system is defined and studied for a coupled system of wave equations with the same wave speed or with different wave speeds.

关键词： Synchronizable system Synchronization solution coupled system of wave equations Exact boundary synchronization