2005-Oujda International Conference on Nonlinear Analysis,
Oujda, Morocco.
Electronic Journal of Differential Equations,
Conference 14 (2006), pp. 135-147. 

Title: Optimal controls for a class of nonlinear evolution systems

Authors: Abdelhaq Benbrik  (Univ. Mohammed 1er, Oujda, Maroc)
         Mohammed Berrajaa (Univ. Mohammed 1er, Oujda, Maroc)
	 Samir Lahrech     (Univ. Mohammed 1er, Oujda, Maroc)  
 
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.