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Exact Controllability of Semilinear Evolution Systems and Its Application

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Abstract

In this paper, we obtain several abstract results concerning the exact controllability of semilinear evolution systems. First, we prove the null local exact controllability of semilinear first-order systems by means of the contraction mapping principle; in this case, we do not assume any compactness. Next, we derive the global and/or local exact controllability of semilinear second-order systems by means of the Schauder fixed-point theorem; in this case, we assume only the embedding of the related spaces having some compactness, which is reasonable for many concrete problems. Our main result shows that the observability of the dual of the linearized system implies the exact controllability of the original semilinear system. Finally, we apply our abstract results to the exact controllability of the semilinear wave equation.

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Authors and Affiliations

  1. Institute of Mathematics, Fudan University, Shanghai, China

    X. Zhang (Assistant Professor)

  2. School of Mathematics, Sichuan University, Chengdu, China

    X. Zhang (Assistant Professor)

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  1. X. Zhang
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Zhang, X. Exact Controllability of Semilinear Evolution Systems and Its Application. Journal of Optimization Theory and Applications 107, 415–432 (2000). https://doi.org/10.1023/A:1026460831701

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  • DOI: https://doi.org/10.1023/A:1026460831701

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