Optimal polynomial decay for a Timoshenko system with a strong damping and a strong delay

Abstract

In this article, we consider a linear Timoshenko system with a strong damping and a strong constant delay acting on the transverse displacement of the beam. Using the semigroup techniques, we first establish the global well‐posedness result under a condition on the weight of the delayed feedback and the weight of the nondelayed feedback. Then, we show that the system is not exponentially stable even in the case of equal‐speed wave propagations. In this regard, we prove that the solution decays polynomially with rate . And in addition, by recent result due to A. Borichev and Y. Tomilov, we show the optimality of that rate.