S4B1 - Graduate Seminar on Analysis - SoSe 2015 - Mathematical Institute of the University of Bonn

RG Analysis and Partial Differential Equations

S4B1 - Graduate Seminar on Analysis (Summer term 2015)

Dozenten:

Termin:

Monday, 16 (c.t.) - 18

Preliminary meeting: Monday, 09.02., 16:15 pm, SemRaum 0.006

Topic: Blow-up for dispersive equations

In this seminar we will study blow-up solutions to various dispersive equations. It is a striking feature of critical and supercritical equations (the terms will be explained in the seminar) that there are solutions which blow-up in finite time. Blow-up of an analytic solution is related to a break down of the mathematical model. We will be interested in sufficient criteria on initial data for blow-up, as well as in a precise description of the blow-up.

Literature:

Sulem and Sulem: The nonlinear Schroedinger equation, Springer
Shatah and Struwe: Geometric wave equations
Tao: Nonlinear dispersive equations
Sogge: Lectures on non-linear wave equations
Lecture notes by Sigmund Selberg
Notes by Andrew Lawrie

Prerequests:

Basic knowledge in Fourier transform, Partial differential equations, Harmonic analysis

Schedule

April 20: Roland Donninger: Wellposedness for nonlinear wave equations
April 27: Tillman Ritschl: Mechanisms of blow-up
May 4: Amos Schickowski: Existence and stability of solitons and concentration compactness I
May 11: Immanuel Zachhuber: Existence and stability of solitons and concentration compactness II
May 18: Tobias Schmidt: Harmonic map heat flow
May 25: public holiday
June 1: Zipeng Rao: The Ljapunov functional of Antonini and Merle
June 8: Wenhui Shi: Uniform blow rates
June 15: Adina Chirila: The heuristics of blow up for NLS (Sulem and Sulem)
June 22: Emil Wiedemann: Blowup for supercritical gKdV
June 29: Gennardy Uralcev: Critical blow-up I
July 6: Lisa Onkes: Critical blow-up II