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<p>We consider the curve diffusion flow for open planar curves with boundary on two skew lines. For each angle <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2021_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="69" /> </InlineMediaObject> <EquationSource Format="TEX">\(\theta \in (0, \pi )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>θ</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mi>π</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> of the two skew lines, we prove the existence of global-in-time solutions under a suitable initial condition. Furthermore, we show the full limit convergence of solutions to the arc of the sector with the central angle <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2021_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation> and the same area as that of the initial curve.</p>

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Curve Diffusion Flow with Boundary on Skew Lines

  • 期刊论文

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  • 发表日期：

    2025年5月10日

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  • Fuya Hiroi,
  • Shinya Okabe

摘要

We consider the curve diffusion flow for open planar curves with boundary on two skew lines. For each angle \(\theta \in (0, \pi )\) θ ∈ ( 0 , π ) of the two skew lines, we prove the existence of global-in-time solutions under a suitable initial condition. Furthermore, we show the full limit convergence of solutions to the arc of the sector with the central angle \(\theta \) θ and the same area as that of the initial curve.