New stability result of a partially dissipative viscoelastic Timoshenko system with a wide class of relaxation function

This paper is concerned with the following partially dissipative viscoelastic Timoshenko system {ρ1ϕtt−κ(ϕx+ψ)x+κ∫0tg(t−s)(ϕx+ψ)xds=0in(0,L)×R+,ρ2ψtt−bψxx+κ(φx+ψ)−κ∫0tg(t−s)(ϕx+ψ)ds=0in(0,L)×R+,with damping mechanism acting only on the shear force, and with Dirichlet boundary conditions. We consider a very general relaxation function g′(t)≤−ξ(t)H(g(t)),∀t≥0.Under appropriate conditions on ξ and H, we establish a general stability result. The result is obtained under the assumption of equal speed of wave propagation. This work extends and generalizes many results in literature such as Alves et al. [On modeling and uniform stability of a partially dissipative viscoelastic Timoshenko system. SIAM J Math Anal. 2019;51(6):4520–4543].