On the Memory-Type Controllability of the Parabolic Equation with a Memory Term

In this paper, we study a new kind of approximate controllability of the parabolic equation with memory called memory-type controllability. Compared to the usual approximate controllability, the new controllability is defined by imposing some additional constraints on the memory term. The key point is to prove that the adjoint system associated to our controlled system satisfies a unique continuation property. Finally, the memory-type controllability is obtained.