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<p>This paper investigates the well-posedness and asymptotic behavior of a suspension bridge system, modeling the deck using Timoshenko–Ehrenfest beam theory with fractional damping. Using semigroup theory, we establish existence and uniqueness via the Lumer–Phillips Theorem, showing that the system’s operator generates a contraction <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="707_2025_4486_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(C_0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>-semigroup. Spectral analysis proves strong stability, while the Gearhart Theorem rules out uniform stability. Finally, polynomial decay is obtained via the Borichev–Tomilov and Batty–Chill–Tomilov Theorems.</p>

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Well-posedness and asymptotic behavior of a suspension bridge system of Timoshenko–Ehrenfest type with fractional derivative damping

  • 期刊论文

  • 发表日期：

    2025年8月28日

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  • Rafael O. de Jesus,
  • Carlos A. Raposo,
  • Carlos A. Nonato,
  • Joilson O. Ribeiro

摘要

This paper investigates the well-posedness and asymptotic behavior of a suspension bridge system, modeling the deck using Timoshenko–Ehrenfest beam theory with fractional damping. Using semigroup theory, we establish existence and uniqueness via the Lumer–Phillips Theorem, showing that the system’s operator generates a contraction \(C_0\) C 0 -semigroup. Spectral analysis proves strong stability, while the Gearhart Theorem rules out uniform stability. Finally, polynomial decay is obtained via the Borichev–Tomilov and Batty–Chill–Tomilov Theorems.