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Exact Controllability of Semilinear Evolution Systems and Its Application

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  • X. Zhang

    (Fudan University
    Sichuan University)

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.

Suggested Citation

  • X. Zhang, 2000. "Exact Controllability of Semilinear Evolution Systems and Its Application," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 415-432, November.
    • Handle: RePEc:spr:joptap:v:107:y:2000:i:2:d:10.1023_a:1026460831701
    DOI: 10.1023/A:1026460831701
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    Citations

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    Cited by:

    1. Nazim Mahmudov, 2013. "Exact null controllability of semilinear evolution systems," Journal of Global Optimization, Springer, vol. 56(2), pages 317-326, June.
    2. Dimplekumar Chalishajar & Annamalai Anguraj & Kandasamy Malar & Kulandhivel Karthikeyan, 2016. "A Study of Controllability of Impulsive Neutral Evolution Integro-Differential Equations with State-Dependent Delay in Banach Spaces," Mathematics, MDPI, vol. 4(4), pages 1-16, October.
    3. B. Radhakrishnan & K. Balachandran, 2012. "Controllability of Neutral Evolution Integrodifferential Systems with State Dependent Delay," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 85-97, April.
    4. B. Liu, 2004. "Controllability of Nonlinear Neutral Evolution Integrodifferential Systems with Infinite Delay," Journal of Optimization Theory and Applications, Springer, vol. 122(1), pages 87-109, July.
    5. Tajani, Asmae & El Alaoui, Fatima-Zahrae & Boutoulout, Ali, 2022. "Regional boundary controllability of semilinear subdiffusion Caputo fractional systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 481-496.
    6. J. P. Dauer & N. I. Mahmudov, 2004. "Controllability of Some Nonlinear Systems in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 319-329, November.

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