Local existence and lower bound of blow-up time to a Cauchy problem of a coupled nonlinear wave equations

Abstract

In this paper, we consider a Cauchy problem of a coupled linearly-damped wave equations with nonlinear sources. In the whole space, we establish the local existence and show that there are solutions with negative initial energy that blow up in a finite time. Moreover, under some conditions on the initial data, we estimate a lower bound of that time.

Keywords

• cauchy problem
• blow up
• negative initial energy
• nonlinear source
• lower bound