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Seminario di Equazioni Differenziali e Applicazioni: (Anti) symmetrization properties for parabolic equations

Lunedì 18 Aprile 2016, ore 12:00 - Aula 2BC30 - Luca Rossi

ARGOMENTI: Seminari

SEMINARIO DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI

Lunedì 18 Aprile 2016 alle ore 12:00 in Aula 2BC30, Luca Rossi (Università di Padova - EHESS Parigi) terrà un seminario dal titolo "(Anti) symmetrization properties for parabolic equations".

Abstract
I will present a classical symmetrization result by Jones which applies to rather general semilinear parabolic equations. A consequence of this result is that the level sets of a solution with compactly supported initial datum stay at bounded Hausdorff distance from a suitable evolving family of spheres. Then, a very natural question is whether such distance tends to zero as time goes to infinity, which would be a truly symmetrization property. A negative answer has been given by Yagisita '01 and Roussier '04 in the case of a bistable reaction-diffusion equation. I will present a counter-exemple in the case of a concave semilinear term.

Rif. Int. M. Bardi, C. Marchi, P. Mannucci

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