RG Analysis and Partial Differential Equations

V5B1 - Advanced Topics in Analysis and PDE (Sommersemester 2013)

Dozent: Prof. Dr. Herbert Koch


    Mittwoch, 8 (c.t.) - 10, Freitag 10 (c.t.) - 12 , Raum 1.007


      We will study dispersive equations, more precisely some of the main examples: the nonlinear Schroedinger equation, the Korteweg-de-Vries equation, and the nonlinear wave equation. The focus will be on the existence of solutions to the initial value problem, and asymptotic properties. Keywords are: Fourier transform, stationary phase, dispersive estimates, functions of bounded p variation, adapted function spaces, solitons.


      Stein: Harmonic analysis:real-variable methods, orthogonality, and oscillatory integrals. Princeton 1993
      Tao: Nonlinear dispersive equations. Local and global analysis. AMS 2006
      Notes Part 1 Part 2