We consider the time optimal control problem for a semilinear parabolic control system, where the target is the closed ball with center 0 and radius R greater than or equal to 0 in a Hilbert space X. In particular, we allow the origin of X to be the target. Using an appropriate Kruzkov-type transformation, we give an existence and uniqueness result for the associated Hamilton - Jacobi Bellman equation, even when the reachable set is not the whole space.