Null Controllability Results for Degenerate Parabolic Equations

The null controllability of parabolic operators in bounded domains, with both boundary or locally distributed controls, is a well-established property, see, e.g., (Bensoussan et al., 1993) and (Fattorini, 1998). Such a property brakes down, however, for degenerate parabolic operators even when degeneracy occurs on ”small” subsets of the space domain, such as subsets of the boundary. This talk will discuss some null controllability results that have been recently obtained for degenerate parabolic operators via new global Carleman estimates. It will be also explained why, in such a context, the use of suitable Hardy-type inequalities becomes essential.