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<p>In this paper, we analyze the stabilization of a wave equation subject to a fractional damping term that varies with time. We begin by proving the well-posedness of the system through the framework of semigroup theory for linear operators. Subsequently, we establish the strong stability of the solution. Furthermore, we derive general estimates for the energy decay rates. The methodology integrates tools from frequency domain analysis and multiplier techniques.</p>

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Asymptotic behavior of the wave equation under time-dependent fractional damping

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年1月5日

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  • Younes Bidi,
  • Saleh Fahad Aljurbua,
  • Ahmed Bchatnia,
  • Abderrahmane Beniani

摘要

In this paper, we analyze the stabilization of a wave equation subject to a fractional damping term that varies with time. We begin by proving the well-posedness of the system through the framework of semigroup theory for linear operators. Subsequently, we establish the strong stability of the solution. Furthermore, we derive general estimates for the energy decay rates. The methodology integrates tools from frequency domain analysis and multiplier techniques.