2005-Oujda International Conference on Nonlinear Analysis, Oujda, Morocco.
Electron. J. Diff. Eqns., Conference 14 (2006), pp. 135-147.

Optimal controls for a class of nonlinear evolution systems

Abdelhaq Benbrik, Mohammed Berrajaa, Samir Lahrech

Abstract:
We consider the abstract nonlinear evolution equation $\dot{z}+ Az =uBz +f$. Viewing $u$ as control, we seek to minimize $J(u)=\int_{0}^{T}L(z(t),u (t))\,dt$. Under suitable hypotheses, it is shown that there exists an optimal control $\overline{u}$ and that it satisfies the appropriate optimality system. An example involving the $p$-Laplacian operator demonstrates the applicability of our results.

Published September 20, 2006.
Math Subject Classifications: 49J20, 49K20.
Key Words: Optimal control; monotone operator; compact embedding; $p$-Laplacian; bilinear system.

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Abdelhaq Benbrik
Département de Mathématiques et Informatique
Faculté des Sciences
Université Mohammed 1er, Oujda, Maroc
email: benbrik@sciences.univ-oujda.ac.ma
Mohammed Berrajaa
Département de Mathématiques et Informatique
Faculté des Sciences
Université Mohammed 1er, Oujda, Maroc
email: berrajaa@sciences.univ-oujda.ac.ma
Samir Lahrech
Département de Mathématiques et Informatique
Faculté des Sciences
Université Mohammed 1er, Oujda, Maroc
email: lahrech@sciences.univ-oujda.ac.ma

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