Controllability of the Impulsive Semilinear Heat Equation with Memory and Delay

For many control systems in real life, impulses and delays are intrinsic properties that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbations of a system do not modify certain properties such as controllability. In other words, the controllability is robust by looking the impulses and delays as perturbations. In this regard, in this paper, we prove the interior approximate controllability of the Impulsive Semilinear Heat Equation with Memory and Delay. This is done by employing A.E. Bashirov and at. technique which avoids fixed point theorems. In this case, the delay helps us to prove the approximate controllability by pulling back the control solution to a fixed curve in a short time interval.