Optimal blowup time of diffusion equations with control

We study the blowup time for semilinear parabolic differential equations with control function by constructing new dynamic programming methodology. This new approach allows us to formulate verification theorem and sufficient optimality conditions of the first order for the controlled blowup time. We define an ϵ-optimal value function and we construct sufficient ϵ-optimal conditions for that function again in terms of new dynamic programming inequality.