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<p>In the paper, we discuss the two-dimensional contact Muskat problem with zero surface tension on a free boundary. The initial shape of the unknown interface is a smooth simple curve which forms acute corners <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="30_2025_1110_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta _{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>δ</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="30_2025_1110_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta _{1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>δ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> with fixed boundaries. Under suitable assumptions on the given data, the one-to-one local classical solvability of this problem is proved. We also describe the sufficient conditions on the data in the model which provide the existence of the “waiting time” phenomenon.</p>

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On a local solvability of the contact Muskat problem

  • 期刊论文

  • 发表日期：

    2025年9月2日

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  • Nataliya Vasylyeva

摘要

In the paper, we discuss the two-dimensional contact Muskat problem with zero surface tension on a free boundary. The initial shape of the unknown interface is a smooth simple curve which forms acute corners \(\delta _{0}\) δ 0 and \(\delta _{1}\) δ 1 with fixed boundaries. Under suitable assumptions on the given data, the one-to-one local classical solvability of this problem is proved. We also describe the sufficient conditions on the data in the model which provide the existence of the “waiting time” phenomenon.