Well-posedness and exponential stability for a shear beam model with a second sound

Abstract

In this manuscript, we consider a beam model called the Shear beam model (no rotary inertia) with a second sound. First, we establish well-posedness findings by applying the Faedo-Galerkin method, and by constructing an appropriate Lyapunov functional, we show exponential decay findings for the solutions of the system. Furthermore, our obtained findings are not related to any relationship between the system parameters.