New general decay results in a finite-memory bresse system

Abstract

This paper is concerned with the following memory-type Bresse system ρ 1 ϕtt − k 1 (ϕx + ψ + lw)x − lk 3 (wx − lϕ) = 0, ρ 2 ψtt − k 2 ψxx + k 1 (ϕx + ψ + lw) + t 0 g(t − s)ψxx(•, s)ds = 0, ρ 1 wtt − k 3 (wx − lϕ)x + lk 1 (ϕx + ψ + lw) = 0, with homogeneous Dirichlet-Neumann-Neumann boundary conditions, where (x, t) ∈ (0, L) × (0, ∞), g is a positive strictly increasing function satisfying, for some nonnegative functions ξ and H, g (t) ≤ −ξ(t)H(g(t)), ∀t ≥ 0. Under appropriate conditions on ξ and H, we prove, in cases of equal and non-equal speeds of wave propagation, some new decay results that generalize and improve the recent results in the literature.

Energy decay of one-dimensional thermoelastic bresse system with distributed neutral delay and a second sound

“…The Bresse system (1.1) reduces to the well-known Timoshenko system where the longitudinal displacement 𝒘 is not considered (𝒍 = 0), on the other hand, the energy associated with this system (1.1) remains constant when the time 𝒕 evolves, because it is an undamped system. That's why, different types of dampings should be added to the equations or at the limit, in order to stabilize this system that has been studied by many authors (see [14,3,4,17]).…”

A new stability result for a thermoelastic Bresse system with viscoelastic damping

“…System (1.1) has been investigated by many authors in the literature, and the results of well-posedness, stability (polynomial and exponential) have been established, see for example results in [1][2][3][4][5][6][7][8][9][10][11][12][13] and the references cited therein. Recently, Messauodi and Hassan [14] considered…”

Existence and energy decay of a Bresse system with thermoelasticity of type III

“…In the last years, the asymptotic stability for the Bresse system has attracted the attention of researchers and various damping mechanisms were considered to obtain exponential stability. Among them, Boussouira et al [2], Copetti et al [5], El Arwadi et al [11], Guesmia and Kirane [16], Messaoudi et al [22], Santos et al [23], Soriano et al [25] and others.…”