Nonlinear stability of self-similar solutions for semilinear wave equations

Abstract

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.

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

References in corpus (2)

• On blowup for semilinear wave equations with a focusing nonlinearity
• Asymptotics and analytic modes for the wave equation in similarity coordinates

Cited by in corpus (4)

• Scattering for radial, semi-linear, super-critical wave equations with bounded critical norm
• Stable ODE-type blowup for some quasilinear wave equations with derivative-quadratic nonlinearities
• The Radial Wave Operator in Similarity Coordinates
• Finite-time degeneration of hyperbolicity without blowup for quasilinear wave equations