Blowup behavior of strongly perturbed wave equations

TL;DR

This paper investigates the blowup behavior of strongly perturbed wave equations with supercritical nonlinearities, demonstrating that the unperturbed ODE blowup profile remains relevant and universal in describing stable blowup in these equations.

Contribution

It shows that the ODE blowup profile persists in strongly perturbed wave equations, establishing the universality of stable blowup behavior in a broad class of semilinear wave equations.

Findings

ODE blowup profile describes stable blowup

Stable blowup is a universal phenomenon

Results apply to a large class of equations

Abstract

We study the blowup behavior of a class of strongly perturbed wave equations with a focusing supercritical power nonlinearity in three spatial dimensions. We show that the ODE blowup profile of the unperturbed equation still describes the asymptotics of stable blowup. As a consequence, stable ODE-type blowup is seen to be a universal phenomenon that exists in a large class of semilinear wave equations.