Cari tutti,
Mercoledì 3 febbraio 2016, alle ore 11:30 presso l'aula Seminari del Dipartimento di Matematica dell'Università di Pisa, il professor
Massimiliano Gubinelli (Institute of Applied Mathematics, University of Bonn)
terrà un seminario dal titolo:
"Weak universality of the stationary KPZ equation".
Abstract: I will discuss a notion of solution for the KPZ equation which has been introduced by Jara and Gonçalves (2010) and later improved by Jara and myself (2013) and goes under the name of energy solutions. In a recent work in collaboration with Perkowski we have recently obtained a uniqueness results for energy solutions. Using energy solutions is possible to prove weak universality results for KPZ: namely that a wide class of one dimensional microscopic interacting particle models with weak asymmetry and in non-equilibrium stationary states have large scale fluctuations described by the KPZ equation.
A seguire, nella stessa aula il dottor
Michele Coghi (Scuola Normale Superiore)
terrà un seminario dal titolo:
"Mean field limit of interacting filaments and vector valued non linear PDEs".
Abstract: Families of N interacting curves are considered, with long range, mean-field type, interaction. A family of curves defines a 1-current, concentrated on the curves, analog of the empirical measure of interacting point particles. This current is proved to converge, as N goes to infinity, to a mean field current, solution of a nonlinear, vector valued, partial differential equation. In the limit, each curve interacts with the mean field current and two different curves have an independence property if they are independent at time zero. This set-up is inspired from vortex filaments in turbulent fluids, although for technical reasons we have to restrict to smooth interaction, instead of the singular Biot-Savart kernel. All these results are based on a careful analysis of a nonlinear flow equation for 1-currents, its relation with the vector valued PDE and the continuous dependence on the initial conditions terrà un seminario dal titolo
Tutti gli interessati sono invitati a partecipare.