General decay results for a viscoelastic wave equation with a variable exponent nonlinearity

Article type: Research Article

Authors: Hassan, Jamilu Hashim^a | Messaoudi, Salim A.^{b; *}

Affiliations: [a] Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, P.O. Box 5046, Dhahran 31261, Saudi Arabia. E-mail: elhashim06@yahoo.com | [b] Department of Mathematics, University of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates. E-mail: smessaoudi@sharjah.ac.ae

Correspondence: [*] Corresponding author. E-mail: smessaoudi@sharjah.ac.ae.

Abstract: In this paper we consider a viscoelastic wave equation with a very general relaxation function and nonlinear frictional damping of variable-exponent type. We give explicit and general decay results for the energy of the system depending on the decay rate of the relaxation function and the nature of the variable-exponent nonlinearity. Our results extend the existing results in the literature to the case of nonlinear frictional damping of variable-exponent type.

Keywords: Viscoelastic, general decay, relaxation function, variable exponent

DOI: 10.3233/ASY-201661

Journal: Asymptotic Analysis, vol. 125, no. 3-4, pp. 365-388, 2021