Veranstaltung

Vortrag
Blow-up and Conley index at infinity
Juliette Hell (FU Berlin)
13.7.2009, 16:30 Uhr – 17:30 Uhr

The partial differential equations arising in geometric analysis often develop singularities corresponding to the blow-up (or finite time explosion) of some quantity. In this talk we will address the main questions arising in the study of blow-up phenomena. Besides the existence of blow-up solutions, one is interested in the shape of the blow-up profiles. How fast does the blow-up takes place? Where do blow-up trajectories come from? A natural strategy to answer such questions is to translate the problem at infinity into a finite problem and apply or adapt some powerful methods to this finite problem. Dynamical systems theory provides useful tools for the analysis of these phenomena, such as the study of stable, unstable, center manifolds or the Conley index techniques for the detection of connecting orbits. These ideas will be discussed as well as illustrated on some examples.

Verknüpft mit:

• Juliette Hell
• Sommersemester 2009