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

被引：19

作者：

Belhannache, Farida ^{[1
]}

Algharabli, Mohammad M. ^{[2
]}

Messaoudi, Salim A. ^{[3
]}

机构：

[1] Mohammed Seddik Ben Yahia Univ Jijel, Dept Math, Jijel, Algeria

[2] King Fahd Univ Petr & Minerals, Preparatory Year Program, Dhahran 31261, Saudi Arabia

[3] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia

来源：

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS | 2020年 / 26卷 / 01期

关键词：

Viscoelasticity; Optimal decay; Relaxation functions; Convexity; DECAY-RATES; WAVE-EQUATION; ENERGY; EXISTENCE; BEHAVIOR; SYSTEM;

D O I：

10.1007/s10883-019-9429-z

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we consider a viscoelastic equation with a nonlinear frictional damping and a relaxation function satisfying g '(t) <= -xi(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).

引用

页码：45 / 67

页数：23

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