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Abstract <p> For a semilinear parabolic partial differential equation, we consider an asymptotic solution that converges to a traveling wave at large times <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2616_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(t\)</EquationSource> </InlineEquation>. The velocity of such a wave is time dependent, and we construct the asymptotics as <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2616_Article_IEq2.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(t\to\infty\)</EquationSource> </InlineEquation>. We find that the asymptotics contains logarithms and cannot be constructed in the form of a power series. </p>

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Asymptotic solution convergence to a traveling wave in the Kolmogorov–Petrovskii–Piskunov equation

  • 期刊论文

  • 发表日期：

    2025年4月25日

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  • L. A. Kalyakin

摘要

Abstract

For a semilinear parabolic partial differential equation, we consider an asymptotic solution that converges to a traveling wave at large times \(t\) . The velocity of such a wave is time dependent, and we construct the asymptotics as \(t\to\infty\) . We find that the asymptotics contains logarithms and cannot be constructed in the form of a power series.