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.

Show me the PDF file (248K), TEX file, and other files for this article.

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

Return to the table of contents for this conference.
Return to the EJDE web page