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<p>The time-fractional wave equations are used to describe anomalous diffusion, sub-diffusion processes and relaxation phenomena in complex viscoelastic materials. In this paper, we study a class of final value problems for a time-fractional wave equations involving Caputo’s fractional derivative of order <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3259_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="74" /> </InlineMediaObject> <EquationSource Format="TEX">\(1&lt;\alpha &lt;2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>&lt;</mo> <mi>α</mi> <mo>&lt;</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> in a bounded domain. Firstly, we establish the ill-posedness of the problem then investigate the filter method of regularization for it. Finally, we propose a numerical example to illustrate our theoretical results.</p>

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Recovering terminal wave amplitude of mechanical diffusive in waves visco-elastic materials

  • 期刊论文

  • 发表日期：

    2025年5月22日

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  • Triet Minh Le,
  • Phong Hong Luu,
  • Hoang Minh Nguyen

摘要

The time-fractional wave equations are used to describe anomalous diffusion, sub-diffusion processes and relaxation phenomena in complex viscoelastic materials. In this paper, we study a class of final value problems for a time-fractional wave equations involving Caputo’s fractional derivative of order \(1<\alpha <2\) 1 < α < 2 in a bounded domain. Firstly, we establish the ill-posedness of the problem then investigate the filter method of regularization for it. Finally, we propose a numerical example to illustrate our theoretical results.