Dottorato in Matematica 28° ciclo SEMINARIO DI DOTTORATO Martedì 30 settembre 2014 ore 15.00 (Aula Seminari di Matematica) Alessio Marinelli Some results on differential nonlocal elliptic and parabolic equations Abstract We present a semilinear elliptic problem driven by the general fractional powers of the negative Laplacian in presence of a generic logistic function having an indefinite weight. In particular we look for the existence and non existence of solutions for the associated Dirichlet problem. In the second part of the talk we start from the classical parabolic result of D.G.Aronson and H.F.Weinberger to present the recent works of H.Berestycki, X.Cabré and J.M.Roquejoffre on the influence of Fractional Diffusion in FisherKPP Equations. Relatore: Andrea Pugliese Dipartimento di Matematica Via Sommarive, 14 38123 Povo (TN), Italy Tel. +39 0461 281625 Fax +39 0461 281624 mail: phd.math@unitn.it
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