The main topic is the analysis of long-time behaviour of solutions to nonlinear dispersive equations (in particular we shall focus on NLS and gKdV). We shall consider the corresponding problems in two different settings:

the euclidean one where we shall mainly address the issue of nonlinear scattering (eventually modified scattering) of nonlinear solutions to linear solutions for large times; and the compact setting where we shall focus on the analysis of the growth of higher order Sobolev norms. Time permitting we shall also present basic results about the blow-up of solutions.

The lectures will be essentially self-contained, only basic knowledges of functional analysis are needed: Lebesgue spaces, Sobolev spaces and Sobolev embedding, Fourier transform.

## Large time behavior of solutions to nonlinear dispersive equations

Lecturer:

Nicola Visciglia

Academic Year:

2017-2018

Period:

January-June

Duration:

20 h

Description:

Research Group:

Location:

A-134