Nonlinear stability of self-similar solutions for semilinear wave equations

Roland Donninger

Published 2008-11-12, updated 2009-12-08Version 2

We prove nonlinear stability of the fundamental self--similar solution of the wave equation with a focusing power nonlinearity $\psi_{tt}-\Delta \psi=\psi^p$ for $p=3,5,7,...$ in the radial case. The proof is based on a semigroup formulation of the wave equation in similarity coordinates.