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Commun. Korean Math. Soc. 2023; 38(3): 943-966
Online first article July 12, 2023 Printed July 31, 2023
https://doi.org/10.4134/CKMS.c220225
Copyright © The Korean Mathematical Society.
Energy decay for a viscoelastic equation with Balakrishnan-Taylor damping involving infinite memory and nonlinear time-varying delay terms in dynamical boundary
soufiane Benkouider, Abita Rahmoune
Amar Telidji University; Amar Telidji University
In this paper, we study the initial-boundary value problem for viscoelastic wave equations of Kirchhoff type with Balakrishnan--Taylor damping terms in the presence of the infinite memory and external time-varying delay. For a certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation function which is not necessarily of exponential or polynomial type. Also, we show another stability with $g$ satisfying some general growth at infinity.
Keywords: Balakrishnan--Taylor damping, general decay rate, time-varying delay, convex function, infinite memory
MSC numbers: Primary 93D15, 74D10, 35L20, 35B40
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