Global Well-Posedness and Exponential Decay of Shear Beam Model Subject to a Neutral Delay

Abstract

In this paper, we consider a one-dimensional system known as Shear beam model (no rotary inertia) where the transverse displacement equation is subject to a distributed delay of neutral type. Under some assumptions on the kernel h, we first achieved the global well- posedness of the system by using the classical Faedo-Galerkin approximations along with two a priori estimates. Next, we find the energy expression and by using technique of Lyapunov functional we demonstrate, although delays are known to be of a destructive nature in the general case, that this system is exponentially stable regardless any relationship between coefficients of the system.