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<p>A nonlocal reaction-diffusion equation governed by a fractional Laplace operator on a bounded domain is studied in this paper. First, the strong convergence of solutions of the equations governed by fractional Laplacian to the solutions of the classical equations governed by a standard Laplace operator is proved, when the fractional parameter grows to <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="245_2025_10242_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Second, for the autonomous case, the upper semicontinuity of global attractors with respect to the attractors of the limit problem is established. Apparently, these are the first results for this kind of problems on bounded domains.</p>

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Strong Convergence of Solutions and Attractors for Reaction-Diffusion Equations Governed by a Fractional Laplacian

  • 期刊论文

  • 发表日期：

    2025年3月8日

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  • Jiaohui Xu,
  • Tomás Caraballo,
  • José Valero

摘要

A nonlocal reaction-diffusion equation governed by a fractional Laplace operator on a bounded domain is studied in this paper. First, the strong convergence of solutions of the equations governed by fractional Laplacian to the solutions of the classical equations governed by a standard Laplace operator is proved, when the fractional parameter grows to \(1\) 1 . Second, for the autonomous case, the upper semicontinuity of global attractors with respect to the attractors of the limit problem is established. Apparently, these are the first results for this kind of problems on bounded domains.