A blow-up result for a Nakao-type weakly coupled system with nonlinearities of derivative-type

TL;DR

This paper proves a blow-up result for a coupled wave and Klein-Gordon system with derivative nonlinearities, showing solutions become unbounded under certain initial conditions using an iteration method.

Contribution

It establishes a blow-up result for a Nakao-type weakly coupled system with derivative nonlinearities, which was not previously known.

Findings

Solutions blow up in finite time for nonnegative, compactly supported initial data.

The blow-up is proved using an iteration argument.

The result extends understanding of blow-up phenomena in coupled wave and Klein-Gordon systems.

Abstract

In this paper, we consider a weakly coupled system of a wave and damped Klein-Gordon equation with nonlinearities of derivative type. We prove a blow-up result for the Cauchy problem associated with this system for nonnegative and compactly supported data by means of an iteration argument.