Lifespan estimates of solutions to quasilinear wave equations with damping and negative mass term

The main goal of this work is to investigate formation of singularities for solutions to the quasilinear wave equations with damping terms, negative mass terms and divergence form nonlinearities in the critical and sub-critical cases. Upper bound lifespan estimates of solutions are derived by applying the rescaled test function method and iteration technique. The results are the same as corresponding wave equation without damping term and mass term. The main new contribution is that lifespan estimates of solutions are associated with the well-known Strauss exponent and Glassey exponent. To the best of our knowledge, the results in Theorems \begin{document}$ 1.1-1.4 $\end{document} are new. Moreover, the changing trends of semilinear wave equations are illustrated through numerical simulation.