# Controllability of the impulsive semi linear beam equation with memory and delay

## TL;DR

This paper investigates the approximate controllability of a semilinear beam equation incorporating impulses, memory, and delay, demonstrating robustness of controllability despite these complexities using a novel technique.

## Contribution

It introduces a fixed-curve pulling back method to establish controllability without fixed point theorems, accounting for impulses and delays.

## Key findings

- Achieved approximate controllability of the system.
- Showed controllability robustness under impulses and delays.
- Developed a new technique avoiding fixed point theorems.

## Abstract

The semilinear beam equation with impulses, memory and delay is considered. We obtain the approximate controllability. This is done by employing a technique that avoids fixed point theorems and pulling back the control solution to a fixed curve in a short time interval. Demonstrating, once again, that the controllability of a system is robust under the influence of impulses and delays.