Null-controllability and Carleman estimates for non-autonomous degenerate PDEs: a climatological application

Inspired by a Budyko-Seller model, we consider non-autonomous degenerate parabolic equations. As a first step, using Kato's Theorem we prove the well-posedness of such problems. Then, obtaining new Carleman estimates for the non-homogeneous non-autonomous adjoint problems, we deduce null-controllability for the original ones. Some linear and semilinear extensions are also considered. We conclude the paper applying the obtained controllability result to the Budyko-Seller model given in the introduction.