Geometric Flows and Geometric Operators

seminar: Para-differential calculus and its applications to hyperbolic problems

speaker: Francesco Fanelli (Institut Camille Jordan - UMR CNRS 5208, Universite Claude Bernard - Lyon 1)

abstract: We consider a wave equation of the type

D_tt u - a D_xx u = f

We suppose that the coefficient a has a very low regularity. If a depends only on the time variable, one can perform the Fourier transform and solve the equation in the phase space. If a depends also on the spaces variables, we need the help of pseudo and para-differential calculus. We will show the main ideas and results of these topics and, in particular, of the Littlewood-Paley decomposition and we'll see how one can use them in the study of the strictly hyperbolic problem. In particular, we will restrict our attention to the case that a is log-lipschitz both in the time and space variables or log-lipschitz in t and log-zygmund in x.

timetable:
Wed 10 Jun, 16:00 - 17:00, Aula Mancini
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