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<p>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 [<CitationRef CitationID="CR7">7</CitationRef>]. 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.</p>

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On the optimal polynomial decay of shear beams under rotational damping

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月30日

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  • Carlos Nonato Silva Nonato,
  • Dilberto Júnior,
  • Luiz Gutemberg Rosário Miranda,
  • Manoel dos Santos

摘要

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.