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

Document Type : Research Paper


Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS). University of 20 August 1955, 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.


Volume 14, Issue 1
January 2023
Pages 1977-1988
  • Receive Date: 10 June 2022
  • Revise Date: 07 December 2022
  • Accept Date: 12 December 2022