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<p>This work deals with the well-posedness and asymptotic behavior of a Shear beam model subject to internal dissipation of the fractional derivative-type. The energy functional is presented, and the dissipative property of the system is stablished. We use the semigroup theory in order to deal with the well-posedness and we prove the strong stability of the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10659_2025_10156_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mn>0</mn> </msub> </math></EquationSource> <EquationSource Format="TEX">$C_{0}$</EquationSource> </InlineEquation>-semigroup using the Arendt-Batty and Lyubich-Vũ’s general criterion and also we prove the polynomial stability result applying Borichev and Tomilov’s theorem.</p>

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Shear Beam Model with Fractional Derivative-Type Internal Dissipation

  • 期刊论文

  • 发表日期：

    2025年7月30日

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  • Wilson Oliveira,
  • Sebastião Cordeiro,
  • Carlos Alberto Raposo,
  • Dilberto Almeida Júnior

摘要

This work deals with the well-posedness and asymptotic behavior of a Shear beam model subject to internal dissipation of the fractional derivative-type. The energy functional is presented, and the dissipative property of the system is stablished. We use the semigroup theory in order to deal with the well-posedness and we prove the strong stability of the C 0 $C_{0}$ -semigroup using the Arendt-Batty and Lyubich-Vũ’s general criterion and also we prove the polynomial stability result applying Borichev and Tomilov’s theorem.