%0 Journal Article %T Optimal controls for a class of nonlinear evolution systems %A Abdelhaq Benbrik %A Mohammed Berrajaa %A Samir Lahrech %J Electronic Journal of Differential Equations %D 2006 %I Texas State University %X 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. %K Optimal control %K monotone operator %K compact embedding %K $p$-Laplacian %K bilinear system. %U http://ejde.math.txstate.edu/conf-proc/14/b1/abstr.html