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

## TL;DR

This paper investigates conditions under which solutions to strongly damped wave equations in exterior domains become unbounded in finite time, focusing on the influence of initial data and the nonlinearity exponent p.

## Contribution

It establishes blow-up results for strongly damped wave equations in exterior domains, providing new insights into the conditions leading to finite time blow-up.

## Key findings

- Blow-up occurs under certain initial data conditions.
- The exponent p influences the blow-up behavior.
- Results extend understanding of damping effects in exterior domains.

## Abstract

We consider the initial boundary value problem in exterior domain for strongly damped wave equations with power type nonlinearity |u|^p. We will establish blow-up results under some conditions on the initial data and the exponent p.