Global Existence and General Decay of a Weakly Nonlinear Damped Timoshenko System of Thermoelasticity of Type III with Infinite Memory - Houasni, Mohamed; Zitouni, Salah; Djebabla, Abdelhak (Journal of Applied Nonlinear Dynamics, 2026)
In this work, we consider a one-dimensional Timoshenko system of thermoelasticity of type III with infinite memory damped by weakly nonlinear feedbacks. Under suitable conditions, we establish the well-posedness of the problem using semigroups theory, and a general stability estimates using the multiplier method with no growth assumption on $f$ at the origin and without assuming equal or nonequal speeds of propagation of waves which is mentioned in numerous works (e.g. \cite{ayadi,chen,Fareh,jh,hao,masap}). Our results show that the damping effect leads to general decay rate for the energy function and also remove the necessity of the assumption on equal speeds which has been imposed in the prior literature.