Multiplicative controllability for nonlinear degenerate parabolic equations
Dr. Giuseppe Floridia, Università Mediterranea di Reggio Calabria
Aula Beltrami, Dipartimento di Matematica – Martedì 21 Gennaio 2020 h.15:00
Abstract. In this talk we present some approximate controllability results for semilinear degenerate reaction-diffusion equations governed via the variable coefficient of the reaction term (multiplicative control). Before, we considered a one-dimensional uniformly parabolic problem (see ). For this kind of parabolic equations there are some important obstructions to the multiplicative controllability due to the strong maximum principle, thus two kinds of controllability are worth studying: nonnegative controllability (see ) and controllability between sign-changing states (see ). Then, we are able to extend the above results to a class of degenerate reaction-diffusion equations (see ) with application to some energy balance models in climatology (see, e.g., the Budyko-Sellers model).
 P. Cannarsa, G. Floridia, A.Y. Khapalov, Multiplicative controllability for semilinear reaction-diffusion
equations with finitely many changes of sign, Journal de Mathématiques Pures et Appliquées, 108, (2017)
 G. Floridia, Approximate controllability for nonlinear degenerate parabolic problems with bilinear
control, J. Differential Equations, 257 no.9 (2014), 3382-3422.
 G. Floridia, C. Nitsch, C. Trombetti, Multiplicative controllability for nonlinear degenerate parabolic
equations between sign-changing states, to appear on ESAIM COCV, https://arxiv.org/abs/1710.00690.