Controllability for semilinear heat equation with globally Lipschitz nonlinearities and memory term

Abstract

In this paper, we investigate the controllability for a semilinear heat equation with memory and internal control in a bounded domain of Rn. The semilinearity has gradient terms and is globally Lipschitzian. Since memory term does not allow applying Fabre’s unique continuation theorem directly, we made certain adjustments to the terms of the equation. Additionally, the proof of the controllability uses a variant of a classic fixed point method and a technique due to Zuazua and Fabre-Puel-Zuazua.