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Controllability of Some Nonlinear Systems in Hilbert Spaces

Author

Listed:
  • J. P. Dauer

    (University of Tennessee at Chattanooga)

  • N. I. Mahmudov

    (Eastern Mediterranean University)

Abstract

In this paper, several abstract results concerning the controllability of semilinear evolution systems are obtained. First, approximate controllability conditions for semilinear systems are obtained by means of a fixed-point theorem of the Rothe type; in this case, the compactness of the linear operator is assumed. Next, the exact controllability of semilinear systems with nonlinearities having small Lipschitz constants is derived by means of the Banach fixed-point theorem; in this case, the compactness of the operators is not assumed. In both cases, it is proven that the controllability of the linear system implies the controllability of the associated semilinear system. Finally, these abstract results are applied to the controllability of the semilinear wave and heat equations.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:123:y:2004:i:2:d:10.1007_s10957-004-5151-3
    DOI: 10.1007/s10957-004-5151-3
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. L. W. Wang, 2009. "Approximate Controllability for Integrodifferential Equations with Multiple Delays," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 185-206, October.

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