Finite time blow up for wave equations with strong damping in an exterior domain

TL;DR

This paper investigates conditions under which solutions to semilinear wave equations with strong damping in exterior domains blow up in finite time, especially when the nonlinearity exponent is below or equal to Strauss' critical exponent.

Contribution

It extends blow-up results for semilinear wave equations with damping to exterior domains, matching known results in the whole space case.

Findings

Blow-up occurs for p ≤ Strauss' exponent in exterior domains.

Finite time blow-up is established for certain initial conditions.

Results align with known blow-up thresholds in unbounded spaces.

Abstract

We consider the initial boundary value problem in exterior domain for semilinear wave equations with power-type nonlinearity |u| p. We will establish blow-up results when p is less than or equal to Strauss' exponent which is the same one for the whole space case R n .