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Journal of Dynamical and Control Systems

Erschienen in:

18.01.2019

Asymptotic Stability for a Viscoelastic Equation with Nonlinear Damping and Very General Type of Relaxation Functions

verfasst von: Farida Belhannache, Mohammad M. Algharabli, Salim A. Messaoudi

Erschienen in: Journal of Dynamical and Control Systems | Ausgabe 1/2020

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Abstract

In this paper, we consider a viscoelastic equation with a nonlinear frictional damping and a relaxation function satisfying g′(t) ≤ −ξ(t)G(g(t)). Using the Galaerkin method, we establish the existence of the solution and prove an explicit and general decay rate results, using the multiplier method and some properties of the convex functions. This work generalizes and improves earlier results in the literature. In particular, those of Messaoudi (2016) and Mustafa (Math Methods Appl Sci. 2017;V41:192–204).

Vorheriger Artikel Periodic Solutions of a Class of Non-autonomous Discontinuous Second-Order Differential Equations

Nächster Artikel Gevrey Properties and Summability of Formal Power Series Solutions of Some Inhomogeneous Linear Cauchy-Goursat Problems

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Titel: Asymptotic Stability for a Viscoelastic Equation with Nonlinear Damping and Very General Type of Relaxation Functions
verfasst von: Farida Belhannache
Mohammad M. Algharabli
Salim A. Messaoudi
Publikationsdatum: 18.01.2019
Verlag: Springer US
Erschienen in: Journal of Dynamical and Control Systems / Ausgabe 1/2020
Print ISSN: 1079-2724
Elektronische ISSN: 1573-8698
DOI: https://doi.org/10.1007/s10883-019-9429-z

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