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<p>We present the results of determination and investigation of the classical fundamental solution of the Cauchy problem for a class of degenerate parabolic Kolmogorov-type equations with <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7582_Article_IEq1.gif" Format="GIF" Height="24" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(\overrightarrow{2b}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <mn>2</mn> <mi>b</mi> </mrow> <mo stretchy="false">→</mo> </mover> </math></EquationSource> </InlineEquation> -parabolic principal part in the main variables and two groups of spatial variables of degeneration and the coefficients that depend on all variables. The estimates for the classical fundamental solution and its derivatives are obtained.</p>

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On the Classical Fundamental Solution of the Cauchy Problem for One Class of Degenerate Parabolic Equations

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • I. P. Medynsky

摘要

We present the results of determination and investigation of the classical fundamental solution of the Cauchy problem for a class of degenerate parabolic Kolmogorov-type equations with \(\overrightarrow{2b}\) 2 b → -parabolic principal part in the main variables and two groups of spatial variables of degeneration and the coefficients that depend on all variables. The estimates for the classical fundamental solution and its derivatives are obtained.