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<p>In this work, we investigate the global existence of solutions for a singular <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2585_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(p\)</EquationSource> </InlineEquation>-Kirchhoff diffusion equation with logarithmic nonlinearity. Under suitable conditions, we establish the existence of weak solutions by applying energy estimates in combination with Sobolev inequalities and the Galerkin method. Furthermore, we obtain the properties of the extinction and non-extinction of global weak solutions.</p>

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On global weak solutions for a singular Kirchhoff parabolic problem involving logarithmic nonlinearity

  • 期刊论文

  • 发表日期：

    2025年9月26日

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  • Ihya Talibi,
  • Brahim El Boukari,
  • Jalila El Ghordaf

摘要

In this work, we investigate the global existence of solutions for a singular \(p\) -Kirchhoff diffusion equation with logarithmic nonlinearity. Under suitable conditions, we establish the existence of weak solutions by applying energy estimates in combination with Sobolev inequalities and the Galerkin method. Furthermore, we obtain the properties of the extinction and non-extinction of global weak solutions.