New decay results for a viscoelastic-type Timoshenko system with infinite memory

This paper is concerned with the following memory-type Timoshenko system {ρ1φtt-K(φx+ψ)x=0,ρ2ψtt-bψxx+K(φx+ψ)+∫0+∞g(s)ψxx(t-s)ds=0,with Dirichlet boundary conditions, where g is a positive nonincreasing function satisfying, for some nonnegative functions ξ and G, g′(t)≤-ξ(t)G(g(t)),∀t≥0.Under appropriate conditions on ξ and G, we establish some new decay results that generalize and improve many earlier results in the literature such as Mustafa (Math Methods Appl Sci 41(1): 192–204, 2018), Messaoudi et al. (J Integral Equ Appl 30(1): 117–145, 2018) and Guesmia (Math Model Anal 25(3): 351–373, 2020). We consider the equal speeds of propagation case, as well as the nonequal-speed case. Moreover, we delete some assumptions on the boundedness of initial data used in many earlier papers in the literature.