Asymptotic Behaviour of a Viscoelastic Timoshenko System With Infinite Memory Coupled on the Shear Force

We examine a viscoelastic Timoshenko system with infinite memory terms affecting the shear force. We demonstrate that the system remains stable for a wide class of relaxation functions and establish a relationship between the decay rate of the solutions and the growth of g at infinity. We derive a general decay result using the multiplier method with some additional arguments. Our findings expand upon and enhance several previous results in the literature.