Herbstsemester 2010
Wilhelm Schlag
(University of Chicago)
On long-term behavior of solutions to nonlinear evolution equations

After a review of the basics of the existence/uniqueness theory of solutions to subcritical evolution equations of the wave/Schroedinger/Klein-Gordon type, we will then study special soliton solutions, and discuss their stability. We will review some of the classical work on stability versus blow-up. The distinction between focusing and defocusing will be emphasized, and we will concentrate more on the former. We will introduce the notion of a center-stable manifold near soliton type solutions, and prove results on the blow-up/scattering dichotomy. Some ideas of the Kenig-Merle method will be presented.

Zeit:       Mi 10:15 - 12:00 (to be confirmed)
Ort:        HG G 43 (Hermann-Weyl-Zimmer) (to be confirmed)
Beginn:   September 29 (to be confirmed)

M. Struwe