We deal with optimal control problems governed by semilinear parabolic type equations and in particular described by variational inequalities. We will also characterize the optimal controls by giving necessary conditions for optimality by proving the Gâteaux differentiability of solution mapping on control variables.
"Optimal Control Problems for Nonlinear Variational Evolution Inequalities." Abstr. Appl. Anal. 2013 (SI23) 1 - 10, 2013. https://doi.org/10.1155/2013/724190