On the decay and blow up of solutions for a quasilinear hyperbolic equations with nonlinear damping and source terms

摘要

In this work we investigate the global existence, decay, and blow up of solutions for a quasilinear hyperbolic equation. We prove the decay estimates of the energy function by using Nakao’s inequality. Also, we obtain the blow up of solutions and lifespan estimates in three different ranges of the initial energy.