Approximated controllability of the strongly damped impulsive semilinear wave equation with memory and delay

This article studies the interior approximated controllability of the strongly damped semilinear wave equation with memory, impulses and delay terms. The problem is challenging since the state equation contains memory and impulsive terms yielding to potential unbounded control sequences when steering the system to a neighborhood of the final state, thus fixed point theorems cannot be used directly. As alternative, the A.E Bashirov and et al. techniques are applied and together with the delay allowing the control solution to be directed to fixed curve in a short time interval and achieve our result.