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Large time behavior of solutions to nonlinear dispersive equations

Lecturer: 
Nicola Visciglia
Academic Year: 
2017-2018
Period: 
January-June
Duration: 
20 h
Description: 

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. 

Location: 
A-133
Next Lectures: 
Monday, June 4, 2018 - 11:00 to 13:00
Tuesday, June 5, 2018 - 11:00 to 13:00
Wednesday, June 6, 2018 - 11:00 to 13:00
Thursday, June 7, 2018 - 11:00 to 13:00
Friday, June 8, 2018 - 11:00 to 13:00

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