About well-posedness and lack of exponential stability of Shear beam models

In this paper, we consider the Shear beam model (no rotary inertia) and we stablished a decay result of the total energy of solutions by taking a feedback law acting on angle rotation. Unlike the dissipative Shear beam model with damping effect acting on vertical displacement, where the exponential decay holds irrespective any relationship between coefficients of the system, here we prove that system is non-exponential stability by using semigroup techniques. Also, the well-posedness is achieved by using semigroup theory. © 2022, The Author(s) under exclusive license to Università degli Studi di Ferrara.