Second-order optimality conditions for time-optimal control problems governed by semilinear parabolic equations

A class of time-optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints and final point constraints is considered. By introducing the locally optimal solution to time-optimal control problems, we derive first- and second-order necessary optimality conditions of KKT-type and second-order sufficient conditions for locally optimal solutions to the problem and establish regularity of Lagrange multipliers.