We consider a Timoshenko system with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions. We prove that the energy decay with the same rate of decay of the relaxation functions, that is, the energy decays exponentially when the relaxation functions decays exponentially and polynomially when the relaxation functions decays polynomially.
"Decay rates for solutions of a Timoshenko system with a memory condition at the boundary." Abstr. Appl. Anal. 7 (10) 531 - 546, 26 September 2002. https://doi.org/10.1155/S1085337502204133