Controllability of a quasi-linear heat equation

Abstract

In this article we have examined the controllability of the quasi-linear heat equation. We considered distributed controls with support in a small sub-domain. We assumed that the quasi-linear terms are locally Lipschitz. We have proved that there exists a control that drives to desired state within a finite time. Our main objective was to determine the existence, uniquiness and regularity of solutions of controllability of a quasi-linear heat equation