Past lectures

Abstract

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.