Global existence and exponential stability of coupled Lamé system with distributed delay and source term without memory term

In this paper, we prove the global existence and exponential energy decay results of a coupled Lamé system with distributed time delay, nonlinear source term, and without memory term by using the Faedo–Galerkin method. In addition, an appropriate Lyapunov functional, more general relaxation function...

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Bibliographic Details
Published in:	Boundary value problems Vol. 2020; no. 1; pp. 1 - 21
Main Authors:	Boulaaras, Salah, Doudi, Nadjat
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 30-11-2020 Hindawi Limited SpringerOpen
Subjects:	Analysis Approximations and Expansions Delay function Difference and Functional Equations Distributed delay Exponential decay Functionals Galerkin method Lyapunov functional Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations Time lag Viscoelastic term Lyapunov functional 74G25 26A51 35L90 35B40 Delay function Viscoelastic term Exponential decay Distributed delay
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Summary:	In this paper, we prove the global existence and exponential energy decay results of a coupled Lamé system with distributed time delay, nonlinear source term, and without memory term by using the Faedo–Galerkin method. In addition, an appropriate Lyapunov functional, more general relaxation functions, and some properties of convex functions are considered.
ISSN:	1687-2770 1687-2762 1687-2770
DOI:	10.1186/s13661-020-01471-9