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### Multiplicative controllability for nonlinear degenerate parabolic equations

##### Dr. Giuseppe Floridia, Università Mediterranea di Reggio Calabria

Aula Beltrami, Dipartimento di Matematica - Tuesday, January 21, 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 [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.

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