Approximate controllability of semi-linear heat equation with Non-instantaneous impulses, memory and delay

The semilinear heat equation with non-instantaneous impulses $\mathbf{\text{(NII)}}$, memory, and delay is considered and its approximate controllability is obtained. This is done by employing a technique that avoids fixed point theorems and pulls back the control solution to a fixed curve in a short time interval. We demonstrate, once again, that the controllability of the system is robust under the influence of non-instantaneous impulses, memory, and delays. Finally, we present some open problems and a possible general framework to study the controllability of non-instantaneous impulses semilinear systems.