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Optimal Control Problems for Evolution Equations of Parabolic Type with Nonlinear Perturbations

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Abstract

In this paper, we study the optimal control problems governed by the semilinear parabolic type equation in Hilbert spaces. Under Lipschitz continuity condition of the nonlinear term, we can obtain the optimal conditions and maximal principles for a given equation, which are described by the adjoint state corresponding to the given equation without the rigorous conditions for the nonlinear term.

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Authors and Affiliations

  1. Department of Applied Mathematics, Pukyong National University, Busan, 608-737, South Korea

    Jin-Mun Jeong, Eun-Young Ju & Su-Jin Cheon

Authors
  1. Jin-Mun Jeong
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  2. Eun-Young Ju
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  3. Su-Jin Cheon
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Corresponding author

Correspondence to Jin-Mun Jeong.

Additional information

Communicated by Mark J. Balas.

This research was supported by Basic Science Research Program through the National research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0021568).

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Jeong, JM., Ju, EY. & Cheon, SJ. Optimal Control Problems for Evolution Equations of Parabolic Type with Nonlinear Perturbations. J Optim Theory Appl 151, 573–588 (2011). https://doi.org/10.1007/s10957-011-9866-7

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  • DOI: https://doi.org/10.1007/s10957-011-9866-7

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