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Generalized approximate boundary synchronization for a coupled system of wave equations
Author(s) -
Wang Yanyan
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7111
Subject(s) - mathematics , synchronization (alternating current) , boundary (topology) , boundary value problem , dirichlet boundary condition , mathematical analysis , topology (electrical circuits) , combinatorics
In this paper, we consider the generalized approximate boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls. We analyze the relationship between the generalized approximate boundary synchronization and the generalized exact boundary synchronization, give a sufficient condition to realize the generalized approximate boundary synchronization and a necessary condition in terms of Kalman's matrix, and show the meaning of the number of total controls. Besides, by the generalized synchronization decomposition, we define the generalized approximately synchronizable state and obtain its properties and a sufficient condition for it to be independent of applied boundary controls.