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

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Advances in the Theory of Nonlinear Analysis and its Application
Volume: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 : 23 | Download : 6

Publication Date : 2018-09-30

Article Type : Research Paper

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

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