Pontryagin's Principle for State-Constrained Control Problems Governed by Parabolic Equations with Unbounded Controls

This paper deals with optimal control problems governed by semilinear parabolic equations with pointwise state constraints and unbounded controls. Under some strong stability assumption, we obtain necessary optimality conditions in the form of a Pontryagin's minimum principle in qualified form. A Pontryagin's principle in nonqualified form is also proved without any stability condition.