Global existence and polynomial decay for a problem with Balakrishnan-Taylor damping

Abderrahmane Zaraï and Nasser-eddine Tatar

Cheikh El Arbi Tébessi University, 12002 Tébessa, Algeria
King Fahd University of Petroleum and Minerals, Department of Mathematics and Statistics, Dhahran 31261, Saudi Arabia


Abstract: A viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping is considered. Using integral inequalities and multiplier techniques we establish polynomial decay estimates for the energy of the problem. The results obtained in this paper extend previous results by Tatar and Zaraï [Tatar, N-e. and Zaraï, A., Exponential stability and blow up for the problem with Balakrishnan-Taylor damping, to appear in Demonstratio Math.].

AMSclassification: primary 35L20; secondary 35B40, 45K05.

Keywords: Balakrishnan-Taylor damping, polynomial decay, memory term, viscoelasticity.