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).
| Original language | English |
|---|---|
| Pages (from-to) | 45-67 |
| Number of pages | 23 |
| Journal | Journal of Dynamical and Control Systems |
| Volume | 26 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Jan 2020 |
Bibliographical note
Publisher Copyright:© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- Convexity
- Optimal decay
- Relaxation functions
- Viscoelasticity
ASJC Scopus subject areas
- Control and Systems Engineering
- Algebra and Number Theory
- Numerical Analysis
- Control and Optimization
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