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<p>In this paper, we consider a degenerate beam equation that is stabilized with a boundary damping subjected to a time-delay. At first, by means of the semigroup theory, we prove that the considered system is well-posed in suitable weighted spaces. Thereafter, sufficient conditions are proposed in order to ensure that the energy of the system decays exponentially to zero with an explicit and precise decay rate estimate. Our method of proof relies essentially on the construction of a specific Lyapunov functional.</p>

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Stabilization of a degenerate Euler-Bernoulli beam model under boundary time-delayed damping

  • 期刊论文

  • 发表日期：

    2026年6月23日

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  • Jawad Salhi,
  • Mohamed Azzaoui,
  • Mouhcine Tilioua

摘要

In this paper, we consider a degenerate beam equation that is stabilized with a boundary damping subjected to a time-delay. At first, by means of the semigroup theory, we prove that the considered system is well-posed in suitable weighted spaces. Thereafter, sufficient conditions are proposed in order to ensure that the energy of the system decays exponentially to zero with an explicit and precise decay rate estimate. Our method of proof relies essentially on the construction of a specific Lyapunov functional.