Lifespan Estimates of Solutions for a Coupled System of Wave Equations with Damping terms and Negative Mass terms ∗

Abstract

The main purpose of this paper is to study the formation of singularity for a coupled system of wave equations with damping terms, negative mass terms, and divergence form nonlinearities. Upper bound lifespan estimates of solutions to the system are obtained by using the iteration method. The results are the same as the corresponding coupled system of the wave equation with power nonlinearities ${\left|v\right|}^p$ and ${\left|u\right|}^q$ . To the best of our knowledge, the results in Theorems 1–5 are new. In addition, the variation trend of the wave is analyzed by using numerical simulation.