Stability of a viscoelastic Timoshenko system with non-monotonic kernel

Abstract

In this paper, the stability of a linear Timoshenko beam system involved with infinite memory is considered. Different from the previous results on where the monotony of kernel is always fulfilled, the memory kernel under consideration is assumed to be non-monotonic. The well-posedness of the system is obtained by means of resolvent family theory and the exponential stability is proved under certain conditions. Numerical simulations are also presented to verify the main results.