Dilberto Da Silva Almeida Junior

This study investigates the dynamic behavior of a shear beam model incorporating Kelvin‐Voigt type damping. The well‐posedness of the system is established via the Faedo–Galerkin method, ensuring the existence and uniqueness of weak solutions. Subsequently, for the stabilization analysis, an energy perturbation technique is employed. It is shown that the system exhibits exponential stability when the Kelvin‐Voigt mechanism acts either on both the shear force and bending moment, or exclusively on the shear force. In contrast, if the Kelvin‐Voigt damping is applied solely to the bending moment, the system exhibits only polynomial decay. Owing to the absence of rotational inertia in the shear model, the governing equation for the angle of rotation takes an elliptic form, thereby precluding exponential decay under such partial damping. This intrinsic structural property is briefly discussed from a physical perspective.

In this paper, we study the long-time behavior of solutions to the Shear beam model without rotational inertia, where a dissipative mechanism acts only on the equation governing the rotations of the cross-sections. Owing to the elliptic-hyperbolic structure of the system, we prove that the energy decays at a sharp polynomial rate. The optimality is established through resolvent estimates on the imaginary axis based on important arguments of [7]. This result contributes to the stabilization theory of partially damped beam models and settles an important open question concerning the asymptotic behavior in this class of systems.

This paper investigates the one-dimensional truncated version of the porous-elastic system that avoids the damaging con sequences associated with the second frequency spectrum. We consider a feedback law acting on the displacement of the elastic solid and establish well-posedness via the Faedo-Galerkin method. Furthermore, we prove an exponential energy decay result that holds independently of any specific relationship between the system’s coefficients, using the energy perturbation method.

In this paper, we provide necessary and sufficient conditions for obtaining the stabilization properties for the one-dimensional Lord–Shulman thermoelastic theory with porosity subject to microtemperature but without temperature where the microtemperature conduction equations are governed by Cattaneo–Maxwell’s law. Based on recent results due to Bazarra et al., we introduce a stability number[ ] involving all coefficients of the system, and we prove that the exponential decay of the corresponding semigroup holds if and only if [ ]. Otherwise, we show that the system loses exponential stability and its solution decays polynomially with a rate equal to [ ].