Summary: In this paper, we prove the interior approximate controllability of the following semilinear heat equation
where is a bounded domain in , is an open nonempty subset of , and denotes the characteristic function of the set . The distributed control belong to and the nonlinear function is smooth enough and there are , with , such that
where . Under this condition, we prove the following statement: For all open nonempty subset of the system is approximately controllable on . Moreover, we could exhibit a sequence of controls steering the nonlinear system (1) from an initial state to an neighborhood of the final state at time , which is very important from a practical and numerical point of view.