Polynomial Decay Rate for a Coupled Lamé System with Viscoelastic Damping and Distributed Delay Terms

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.

A New Result of Stability for Thermoelastic-Bresse System of Second Sound Related with Forcing, Delay, and Past History Terms

“…The proof of the stability for our system is based on the following lemmas: Lemma 5. Let ðφ, ψ, w, θ, q, z, η t Þ be the solution of ( 19)- (21). Then, the energy functional, defined by (55), satisfies…”

“…Lemma 14. Let ðφ, ψ, w, θ, q, z, η t Þ be the solution of ( 19)- (21). Then, we define the functional…”