Seminario di Equazioni Differenziali e Applicazioni: “Strong competition versus fractional diffusion”

Giovedì 15 Settembre 2016, ore 12:15 - Aula 2BC30 - Gianmaria Verzini


Giovedì 15 Settembre 2016 alle ore 12:15 in Aula 2BC30, Gianmaria Verzini (Politecnico di Milano) terrà un seminario dal titolo “Strong competition versus fractional diffusion”.

Different phenomena can be modeled by elliptic systems involving a number of densities subject to diffusion, reaction and competitive interaction. Relevant particular cases include the Lotka-Volterra competition, widely used in population dynamics and ecology, and the Gross-Pitaevskii one, which appears in the modeling of Bose-Einstein condensation. When competition prevails, the densities tend to segregate each other, and a typical question regards the common shared regularity (i.e. uniform Holder bounds), uniformly w.r.t. the competition parameter. In this talk, I will first review the theory addressing such issue in the case of standard diffusion. Next I will report on some more recent results, obtained in collaboration with Susanna Terracini (Universit di Torino) and Alessandro Zilio (EHESS-CAMS, Paris), concerning the case of anomalous diffusion, i.e. when the Laplace operator is replaced by the (nonlocal) fractional laplacian.

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

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