On the optimal polynomial decay of shear beams under rotational damping

ANNALI DELL UNIVERSITA DI FERRARA 2026 Open access

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Authors: Carlos Nonato Silva Nonato, Dilberto Júnior, Luiz Gutemberg Rosário Miranda, Manoel J. Dos Santos
DOI: 10.1007/s11565-026-00662-z
Cited by: 1
References: 8

Abstract

Abstract 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.

Fields of Study & Subjects

Stability and Controllability of Differential Equations Contact Mechanics and Variational Inequalities Navier-Stokes equation solutions

Publication details

Journal / source
ANNALI DELL UNIVERSITA DI FERRARA
Publisher
Springer Science and Business Media LLC
Volume
72
Issue
2
Publication date
30 March 2026
Language
EN