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Abstract <p>For the equation <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11982_2025_10477_Article_IEq1.gif" Format="GIF" Height="24" Rendition="HTML" Resolution="72" Type="Linedraw" Width="209" /> </InlineMediaObject> <EquationSource Format="TEX">\( - {{( - y)}^{m}}{{u}_{{xx}}} + {{u}_{{yy}}} - \frac{m}{{2y}}{{u}_{y}} = 0\)</EquationSource> <!--RusMath2570021Mirsaburov-m1--> </InlineEquation> in the characteristic triangle, the unique solvability of the problem with the Bitsadze–Samarsky condition is proven on the segment of degeneracy of the equation and on an internal segment parallel to it and lying inside the domain.</p>

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A Problem with an Analogue of the Bitsadze–Samarskii Condition on the Segment of Degeneracy and an Internal Segment Parallel to It in the Domain for a Certain Class of Degenerate Hyperbolic Equations

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • M. Mirsaburov,
  • D. T. Mamatmuminov

摘要

Abstract

For the equation \( - {{( - y)}^{m}}{{u}_{{xx}}} + {{u}_{{yy}}} - \frac{m}{{2y}}{{u}_{y}} = 0\) in the characteristic triangle, the unique solvability of the problem with the Bitsadze–Samarsky condition is proven on the segment of degeneracy of the equation and on an internal segment parallel to it and lying inside the domain.