Vol. 9, No. 2, 2021

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General decay for a viscoelastic equation with time-varying delay in the boundary feedback condition

Abita Rahmoune

Vol. 9 (2021), No. 2, 127–142

This paper is devoted to the study of the weak viscoelastic equation with memory and nonlinear time-varying delay in the boundary feedback condition. To this aim, we consider a mathematical model which describes the viscoelastic system with memory in a bounded domain. We establish the general decay estimate for the energy by introducing suitable Lyapunov functionals.

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general decay, weak viscoelastic equation, time-varying delay
Mathematical Subject Classification
Primary: 35L70, 35B40
Secondary: 93D15
Received: 4 July 2020
Revised: 24 October 2020
Accepted: 16 February 2021
Published: 17 April 2021

Communicated by Victor A. Eremeyev
Abita Rahmoune
Department of Technical Sciences
University of Laghouat
Laboratory of Pure and Applied Mathematics
University of Laghouat