Approximate Controllability of Semilinear Heat Equation with Noninstantaneous Impulses, Memory, and Delay

Abstract

A semilinear heat equation with noninstantaneous impulses, memory, and delay is studied. Its approximate controllability is obtained by employing a technique that pulls back the control solution into a fixed curve in a short time interval. This technique is a modification of the one used by Bashirov et al. to avoid the use of fixed points, but it only works to prove approximate controllability. This technique can be applied to reaction-diffusion systems that behave like the heat equation, such as the one presented in Oliveira. In the end, we consider some examples to be studied in the future.