Scattering problems with homogeneous asymptotics
- Volker Schlue (University of Melbourne)
Abstract
A classical topic in scattering theory is the relation of incoming to outgoing linear waves that have been scattered by a potential. For nonlinear wave equations, in particular those that arise for models of Einstein's equations, waves are scattered by sources that extend into the wave zone, and lead to slow decay in time. In this talk I present joint work with Hans Lindblad, on the role of homogeneous solutions at time-like infinity, and their relation to homogeneous solutions at space-like infinity, for a scattering theory of wave equations with sources in the wave zone. I will discuss a characterisation of homogeneous degree -1 and -2 solutions, which are particularly relevant for scattering in the presence of masses and charges.