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<p>This paper addresses the issue of well-posedness of solutions to the fractional 1-Laplacian parabolic equation with the right-hand side and initial data in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation> space. We demonstrate that the renormalized solutions of this equation are the distributional solutions. Furthermore, the equivalence between renormalized and entropy solutions for this equation was established by proving the existence and uniqueness of both renormalized and entropy solutions.</p>

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Renormalized and entropy solutions for the fractional 1-Laplacian parabolic equation

  • 期刊论文

  • 发表日期：

    2025年6月11日

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  • DingDing Li,
  • Ying Li,
  • Chao Zhang

摘要

This paper addresses the issue of well-posedness of solutions to the fractional 1-Laplacian parabolic equation with the right-hand side and initial data in \(L^1\) L 1 space. We demonstrate that the renormalized solutions of this equation are the distributional solutions. Furthermore, the equivalence between renormalized and entropy solutions for this equation was established by proving the existence and uniqueness of both renormalized and entropy solutions.