Blow-up for semilinear wave equations with damping and potential in high dimensional Schwarzschild spacetime

TL;DR

This paper investigates the finite-time blow-up of solutions to semilinear wave equations with damping and potential in high-dimensional Schwarzschild spacetime, providing lifespan estimates without support restrictions.

Contribution

It extends blow-up analysis to high-dimensional Schwarzschild spacetime with damping and potential, removing previous support distance assumptions.

Findings

Established upper lifespan bounds for solutions

Demonstrated blow-up occurs without initial support restrictions

Extended previous results to higher dimensions

Abstract

In this work, we study the blow up results to power-type semilinear wave equation in the high dimensional Schwarzschild spacetime, with damping and potential terms. We can obtain the upper bound estimates of lifespan without the assumption that the support of the initial date should be far away from the black hole.