Abir Bounaama - Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS). University of ۲۰ August ۱۹۵۵, Skikda, Algeria
Messaoud Maouni - Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS). University of ۲۰ August ۱۹۵۵, Skikda, Algeria
Amar Ouaoua - Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS). University of ۲۰ August ۱۹۵۵, Skikda, Algeria

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.

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