Mathematical Institute of the University of Bonn

RG Analysis and Partial Differential Equations

V5B1 - Advanced Topics in Analysis and PDE (Summer term 2015)

Lecturer:

Prof. Dr. Herbert Koch

Lectures:

Tuesday, 10 (c.t.) - 12 , Room N0.003

Thursday 10 (c.t.) - 12 , Room N0.003

Contents: Linear and nonlinear dispersive equations

Quantization and wave packets. Local and global wellposedness for nonlinear wave, Schrödinger, Korteweg-de Vries type and wave map equations, solitons and solitary waves, global dynamics, stability, scattering and blow-up.

Literature:

• Koch: Nonlinear dispersive equations in Koch/Tataru/Visan: Dispersive equations and nonlinear waves, Birkhäuser 2014
• Sulem and Sulem: The nonlinear Schrödinger equation. Springer
• Tao: Nonlinear dispersive equations, AMS

Prerequests:

Basic knowledge in PDEs and Harmonic analysis (Fourier transform, stationary phase, Littlewood-Paleytheory, interpolation)

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