Optimal control problems governed by some semilinear parabolic equations

Abstract

This paper is concerned with the optimal control problem for the Keller–Segel equations. That is, as a generalization of Ryu and Yagi (J. Math. Anal. Appl. 256 (2001) 45–66) we derive the optimality conditions for the optimal control problem governed by a semilinear abstract equation of nonmonotone type. Moreover, we prove the uniqueness of the optimal control under some conditions.