Global existence, decay and blow up of solutions for a quasilinear hyperbolic equations with source terms

In this paper, we consider the boundary value problem related to the quasilinear hyperbolic equation with nonlinear source terms. We start by showing the local existence theorem. Then, we prove the global existence and the decay of the energy by using Nakao's inequality, finally we get the finite time blow up of solutions.

Keywords:

Blow up , energy function , quasilinear hyperbolic equation , source terms