Blow-up behavior for the Klein-Gordon and other perturbed semilinear wave equations

TL;DR

This paper investigates the conditions under which solutions to the Klein-Gordon and related perturbed semilinear wave equations blow up in finite time, providing new insights into their dynamic behavior across different dimensions.

Contribution

It establishes blow-up results for Klein-Gordon and perturbed semilinear wave equations in various dimensions, extending previous understanding of solution behaviors.

Findings

Blow-up occurs for superlinear power nonlinearities in Klein-Gordon equations.

Results apply to higher dimensions under radial symmetry.

Provides criteria for finite-time blow-up in perturbed wave equations.

Abstract

We give blow-up results for the Klein-Gordon equation and other perturbations of the semilinear wave equations with superlinear power nonlinearity, in one space dimension or in higher dimension under radial symmetry outside the origin.