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From phenomena of synchronization to exact synchronization and approximate synchronization for hyperbolic systems

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Abstract

In this survey paper, the synchronization will be initially studied for infinite dimensional dynamical systems of partial differential equations instead of finite dimensional systems of ordinary differential equations, and will be connected with the control theory via boundary controls in a finite time interval. More precisely, various kinds of exact boundary synchronization and approximate boundary synchronization will be introduced and realized by means of fewer boundary controls for a coupled system of wave equations with Dirichlet boundary controls. Moreover, as necessary conditions for various kinds of approximate boundary synchronization, criteria of Kalman’s type are obtained. Finally, some prospects will be given.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    TaTsien Li

  2. Shanghai Key Laboratory for Contemporary Applied Mathematic and Nonlinear Mathematical Modeling and Methods Laboratory, Fudan University, Shanghai, 200433, China

    TaTsien Li

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  1. TaTsien Li
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Li, T. From phenomena of synchronization to exact synchronization and approximate synchronization for hyperbolic systems. Sci. China Math. 59, 1–18 (2016). https://doi.org/10.1007/s11425-015-5107-0

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  • DOI: https://doi.org/10.1007/s11425-015-5107-0

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