Local existence and blow up of solutions for a logarithmic nonlinear viscoelastic wave equation with  time-varying delay

Oussama Khaldi; Abdelaziz Rahmoune; Djamel Ouchenane; Fares Yazid

Oussama Khaldi Laboratory of pure and applied mathematics,\\ Amar Teledji University, Laghouat 03000, Algeria.
Abdelaziz Rahmoune Laboratory of pure and applied mathematics,\\ Amar Teledji University, Laghouat 03000, Algeria
Djamel Ouchenane university of Laghouat
Fares Yazid Laboratory of pure and applied mathematics,\\ Amar Teledji University, Laghouat 03000, Algeria

Abstract

In this work, we are interested in a logarithmic nonlinear viscoelastic wave equation with a time-varying delay term in a bounded domain. Using the Faedo-Galerkin approximation, we get the local existence of the solution. Then, under suitable conditions, we prove that solutions blow up in finite time.

Author Biography

Djamel Ouchenane, university of Laghouat

Dr. Djemal Ouchenane

Laboratory of pure Mathematics and Applications, Laghouat, Algeria