Mathematisches Institut der Universität Bonn

Arbeitsgruppe Analysis und Partielle Differentialgleichungen

S4B1 - Graduate Seminar on Analysis (Summer term 2015)

Dozenten:

• Dr. Roland Donninger
• Prof. Dr. Herbert Koch,

Termin:

Monday, 16 (c.t.) - 18 , SemRaum 0.006
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