Journal of Mathematical Physics, Analysis, Geometry 2022, Vol. 18, No. 1, pp. 57–74 doi: https://doi.org/10.15407/mag18.01.057 General Decay Result for a Weakly Damped Thermo-Viscoelastic System with Second Sound Amel Boudiaf and Salah Drabla In this paper, an n-dimensional thermo-viscoelastic system with second sound with a weak frictional damping is considered. We establish an explicit and general decay rate result using some properties of convex functions. Our result is obtained without imposing any restrictive growth assumptions on the frictional damping term. Key words: general decay, weak frictional damping, thermo-viscoelastic system with second sound, convexity Mathematical Subject Classification 2010: 35B37, 35L55, 74D05, 93D15, 93D20 1. Introduction In this paper, we are concerned with the following problem: u tt − k 0 △ u (t) − (μ + λ) ∇ (div u) +  t 0 g (t − s)Δu (s) ds + β ∇θ + α (t) w (u t )=0 in Ω × (0, ∞) , (1.1) cθ t + k div q + β div u t =0 in Ω × (0, ∞) , (1.2) τ 0 q t + q + k∇θ =0 in Ω × (0, ∞) , (1.3) k 0 ∂u ∂ν +(μ + λ) div u × ν −  t 0 g (t − s)(∇u (s)) × ν ds + h (u t )=0 on Γ 1 × (0, ∞) , (1.4) u (·, 0) = u 0 ,u t (·, 0) = u 1 ,θ (·, 0) = θ 0 ,q (·, 0) = q 0 in Ω, (1.5) u =0 on Γ 0 × (0, ∞) , (1.6) θ =0 on ∂ Ω × (0, ∞) , (1.7) where Ω is a bounded domain of R n (n ≥ 1) with a smooth boundary ∂ Ω, such that {Γ 0 ∪ Γ 1 } is a partition of ∂ Ω, with meas (Γ 0 ) > 0,ν is the unit outward normal to ∂ Ω,u = u (x, t) ∈ R n is the displacement vector, θ = θ (x, t) is the dif- ference temperature, q = q (x, t) ∈ R n is the heat flux vector and α, w are specific c  Amel Boudiaf and Salah Drabla, 2022