Exponential stability of Timoshenko type system under Dirichlet-Neumann conditions involving time varying delays

Abstract

In this work, we deal with a linear vibrating system of Timoshenko type in the bounded one dimensional domain under Dirichlet-Neumann boundary conditions driven by variable time delays. Using the approach of the stable family of infinitesimal generators of C₀-semigroups and Kato's norm technique, we show that the system is well posed. Moreover, we prove the exponential stability of the system via the Lyapunov's theorem under the assumption that the propagation speeds are equal.