Open Access

  

Original research article

Blow up and asymptotic behavior for a system of viscoelastic wave equations of Kirchhoff type with a delay term

Author(s):

Fatima Zohra Mahdi, Mohamed Ferhat, Ali Hakem

Laboratory ACEDP, Djillali Liabes University, 22000 Sidi Bel Abbes, Algeria

Advances in the Theory of Nonlinear Analysis and its Applications 2(3), 146-167.
Received: February 4, 2018

  

  

  

Accepted: July 19, 2018

  

Published: August 18, 2018

Abstract

The focus of the current paper is to investigate the initial boundary value problem for a system of viscoelastic wave equations of Kirchhoff type with a delay term in a bounded domain. At first, the energy decay rate is proved by Nakao’s technique and expressed polynomially and exponentially depending on the parameter . However, in the unstable set, for certain initial data, the blow-up of solutions is obtained.

Keywords: Global existence, energy decay, blow-up of solutions, nonlinear damping.

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APA Style

Zohra, M. F., Mohamed, F., & Ali, H. (2018). Blow up and asymptotic behavior for a system of viscoelastic wave equations of Kirchhoff type with a delay term. Advances in the Theory of Nonlinear Analysis and its Application2(3), 146-167.