Abstract
In this paper, we prove a general energy decay results of a coupled Lamé system with distributed time delay. By assuming a more general of relaxation functions and using some properties of convex functions, we establish the general energy decay results to the system by using an appropriate Lyapunov functional.
Highlights
Where Ω is a bounded domain in Rn ðn = 1, 2, 3Þ, with smooth boundary ∂Ω
We extend the general decay result obtained by Feng in [18] to the case of distributed term delay, namely, we will make sure that the result is achieved if the distributed delay term exists
We have proved a general energy decay of a coupled Lamé system with distributed time delay
Summary
We shall be concerned with studying the general decay rate of the following Lamé system in Ω × R+ : ðt ð τ2. Problems that contain viscoelasticity have been addressed, and many results have been found regarding the global existence and stability of solutions (see [2, 9]), under conditions on the relaxation function, whether exponential or polynomial decay. Introducing a distributed delay term makes our problem different from those considered so far in the literature The importance of this term appears in many works, and this is due to the fact that many phenomena depends on their past. It is influence on the asymptotic behavior of the solution for the different types of problems such that. If G is a convex function on 1⁄2a, b, g : Ω → a, b, we have
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