Abstract   This paper deals with the local null control of a free-boundary problem for the classical 1D heat equation with distributed controls, locally supported in space. In the main result we prove that, if the final time   T   is fixed and the initial state is sufficiently small, there exist controls that drive the state exactly to rest at time   t  =  T  .
['Enrique Fernández-Cara', 'J. Límaco', 'Silvano D. B. Menezes']
On the controllability of a free-boundary problem for the 1D heat equation