# Critical criteria of Fujita type for a system of inhomogeneous wave inequalities in exterior domains

## TL;DR

This paper establishes optimal Fujita-type criteria for blow-up of inhomogeneous wave inequalities in exterior domains under various boundary conditions, advancing understanding of nonexistence results in wave systems.

## Contribution

It introduces a unified approach to determine optimal blow-up criteria for inhomogeneous wave inequalities with Dirichlet, Neumann, and mixed boundary conditions.

## Key findings

- Derived optimal blow-up criteria for each boundary condition
- Established nonexistence results for stationary wave systems
- Closed open questions in the theory of wave inequalities

## Abstract

We consider blow-up results for a system of inhomogeneous wave inequalities in exterior domains. We will handle three type boundary conditions: Dirichlet type, Neumann type and mixed boundary conditions. We use a unified approach to show the optimal criteria of Fujita type for each case. Our study yields naturally optimal nonexistence results for the corresponding stationary wave system and equation. We provide many new results and close some open questions.