New general decay results in an infinite memory viscoelastic problem with nonlinear damping

Abstract

This work is concerned with a viscoelastic equation with a nonlinear frictional damping and a relaxation function satisfying g (t) ≤-ξ (t)g p (t), t ≥ 0, 1 ≤ p < 3 2. We establish general decay rate results using the multiplier method and some properties of non-homogeneous ordinary differential inequalities. These results extend and improve many results in the literature.

New general decay result for a system of viscoelastic wave equations with past history

“…Our result is obtained under very general assumption on the relaxation functions and without imposing any boundedness condition on the history function u 0 (•, t). Our results generalizes and improves many results in the literature such as [21,18,2,27]…”

“…under relaxation functions satisfying (1.7) and established a general stability result. Recently, Al-Mahdi and Al-Gharabli [2] considered the following viscoelastic problem:…”

Exponential and polynomial decay results for a swelling porous elastic system with a single nonlinear variable exponent damping: theory and numerics

“…case and proved the exponential decay result provided the wave speeds of the system are equal. Al-Mahdi et al [10] and Apalara [11] studied the case…”

A Stability Result for a Viscoelastic Wave Equation in the Presence of Finite and Infinite Memories

“…In addition, we use a weaker boundedness condition on the history data used in earlier papers such as [17][18][19][20].…”