Tuesday, 21 January 2020, 3 p.m. (sharp),

Dr. Giuseppe Floridia, Università Mediterranea di Reggio Calabria

at the conference room of Dipartimento di Matematica "F. Casorati" - aula Beltrami,in Pavia, will give a lecture titled:

MULTIPLICATIVE CONTROLLABILITY FOR NONLINEAR DEGENERATE PARABOLIC EQUATIONS

At the end a refreshment will be organized.

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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 [1]). 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
[2]) and controllability between sign-changing states (see [1]). Then,
we are able to extend the above results to a class of degenerate
reaction-diffusion equations (see [3]) with application to some energy
balance models in climatology (see, e.g., the Budyko-Sellers model).

References
[1] 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) 425–458.
[2] G. Floridia, Approximate controllability for nonlinear degenerate
parabolic problems with bilinear control, J. Differential Equations,
257 no.9 (2014), 3382-3422.
[3] 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.