Blow-up results for some second order hyperbolic inequalities with a nonlinear term with respect to the velocity

TL;DR

This paper establishes conditions under which certain second order hyperbolic inequalities with nonlinear velocity terms lead to finite-time blow-up, using differential inequality analysis.

Contribution

It introduces a method based on differential inequalities to determine blow-up conditions for semilinear wave inequalities and systems.

Findings

Identifies initial data conditions for finite-time blow-up

Applies method to systems of mixed type

Provides a framework for analyzing blow-up in hyperbolic inequalities

Abstract

We give sufficient conditions on the initial data so that a semilinear wave inequality blows-up in finite time. Our method is based on the study of an associated second order differential inequality. The same method is applied to some semilinear systems of mixed type.