Energy Decay Estimates of a Timoshenko System with Two Nonlinear Variable Exponent Damping Terms

Abstract

This paper is concerned with the asymptotic behavior of the solution of a Timoshenko system with two nonlinear variable exponent damping terms. We prove that the system is stable under some specific conditions on the variable exponent and the equal wave speeds of propagation. We obtain exponential and polynomial decay results by using the multiplier method, and we prove that one variable damping is enough to have polynomial and exponential decay. We observe that the decay is not necessarily improved if the system has two variable damping terms. Our results built on, developed and generalized some earlier results in the literature.