  The paper is concerned with a kind of minimal time control problem for the
heat equation with impulse controls. The purpose of such a problem is to find
an optimal impulse control (among certain control constraint set) steering the
solution of the heat equation from a given initial state to a given target set
as soon as possible. We will first study the existence and uniqueness of
optimal solution for this problem. In the formulation of this problem, there
are two parameters: one is the upper bound of the control constraint and the
other one is the moment of impulse time. Then, we will establish the continuity
of the minimal time function of this problem with respect to the above
mentioned two parameters. Moreover, the convergence of the optimal control is
also discussed.
