On the Controllability of a Free-Boundary Problem for 1D Heat Equation with Local and Nonlocal Nonlinearities

This paper deals with the analysis of the internal control of a free-boundary problem for the 1D heat equation with local and nonlocal nonlinearities. We prove a local null controllability result with distributed controls, locally suported in space. The proof is based on Schauder’s fixed point theorem combined with some appropriate specific estimates.