- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 2 Issue: 3
- Blow up and asymptotic behavior for a system of viscoelastic wave equations of Kirchhoff type with a...
Blow up and asymptotic behavior for a system of viscoelastic wave equations of Kirchhoff type with a delay term
Authors : Mahdi FATİMA ZOHRA, Ferhat MOHAMED, Hakem Ali
Pages : 146-167
Doi:10.31197/atnaa.389865
View : 4 | Download : 2
Publication Date : 2018-09-30
Article Type : Research
Abstract :The focus of the current paper is to investigate the initial boundary value problem for a system of viscoelastic wave equations of Kirchho 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 m. However and 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