Coursebooks 2018-2019

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Dispersive PDEs

MATH-478

Lecturer(s) :

Widmayer Klaus Martin

Language:

English

Summary

This course will give an introduction to some aspects of nonlinear dispersive partial differential equations. These are time evolution problems that arise in many contexts in physics, such as quantum mechanics, electrodynamics, fluid motion and relativity.

Content

The course is aimed to be self-contained, introducing the necessary technical tools along the way.

1. Introduction. What are dispersive equations? How do they arise?

2. Technical Background: Fourier Analysis & Sobolev Spaces

3. Linear Dispersive Equations

4. Semilinear Equations
4.1 Local Theory
4.2 Criticality and Scaling
4.3 Global Theory
4.4 Advanced Topics / More Technical Background

5. Quasilinear Equations
5.1 Method of Spacetime Resonances
5.2 Advanced Topics

Learning Prerequisites

Required courses

A solid foundation in analysis (including measure theory and functional analysis) is necessary. Advanced topics such as harmonic analysis would be helpful, but are by no means required.

Assessment methods

Active participation in the exercise sessions

Oral final examination

In the programs

Reference week

 MoTuWeThFr
8-9     
9-10     
10-11     
11-12     
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22     
Under construction
 
      Lecture
      Exercise, TP
      Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German