The present paper is concerned with the controllability of the equation
where , is an open bounded subset of with the boundary of class , , , is the characteristic function of an open subset of , and is a locally integrable completely monotone kernel. The main result tells us that under some assumptions related to the kernel , the problem (1.1) is approximately controllable. In particular, the approximate boundary controllability of the problem follows:
In the last section the controllability of the one-dimensional linear viscoelasticity equation is studied:
where , and , , , .