Nonlinear stability of self-similar solutions for semilinear wave equations

Details Nonlinear stability of self-similar solutions for semilinear wave equations Nonlinear stability of self-similar solutions for semilinear wave equations

2008-11-12

arxiv.org/abs/0811.1908v2

Communications in Partial Differential Equations. 35(4):669-684, 2010

Mathematics

Analysis of PDEs

References added and minor changes, accepted for publication in Communications in Partial Differential Equations

Scientific paper

10.1080/03605300903575857

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.

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