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
External Lecturer:
Nicola Visciglia
Academic Year:
2017-2018
Period:
January-June
Duration:
20 h
Description:
Research Group:
Location:
A-133