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The Carleman Inequality and Its Application to Periodic Optimal Control Governed by Semilinear Parabolic Differential Equations

Author

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  • G. Wang

    (Huazhong Normal University
    Wuhan Institute of Physics and Mathematics)

  • L. Wang

    (Huazhong Normal University)

Abstract

This paper deals with optimal control problems for semilinear parabolic differential equations, which may be governed by nonmonotone operators and have no global solution, with periodic inputs. The Pontryagin maximum principle is obtained and the Carleman inequality for the backward linearized adjoint system associated with the state system is established.

Suggested Citation

  • G. Wang & L. Wang, 2003. "The Carleman Inequality and Its Application to Periodic Optimal Control Governed by Semilinear Parabolic Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 429-461, August.
    • Handle: RePEc:spr:joptap:v:118:y:2003:i:2:d:10.1023_a:1025459624398
    DOI: 10.1023/A:1025459624398
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    References listed on IDEAS

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    1. V. R. Cabanillas & S. B. de Menezes & E. Zuazua, 2001. "Null Controllability in Unbounded Domains for the Semilinear Heat Equation with Nonlinearities Involving Gradient Terms," Journal of Optimization Theory and Applications, Springer, vol. 110(2), pages 245-264, August.
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    Cited by:

    1. Yueliang Duan & Lijuan Wang, 2020. "Minimal Norm Control Problem Governed by Semilinear Heat Equation with Impulse Control," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 400-418, February.
    2. G. Wang & L. Zhang, 2006. "Exact Local Controllability of a One-Control Reaction-Diffusion System," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 453-467, December.

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