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<p>The paper is devoted to the investigation of the solvability of an integro-differential equation in the case of the double scale anomalous diffusion with a sum of two negative Laplacians in different fractional powers in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40879_2025_854_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb R}^{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation>. The proof of the existence of solutions relies on a fixed point technique. Solvability conditions for the elliptic operators without the Fredholm property in unbounded domains are used.</p>

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Existence of stationary solutions for some integro-differential equations with the double scale anomalous diffusion

  • 期刊论文

  • 发表日期：

    2025年9月8日

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  • Vitali Vougalter,
  • Vitaly Volpert

摘要

The paper is devoted to the investigation of the solvability of an integro-differential equation in the case of the double scale anomalous diffusion with a sum of two negative Laplacians in different fractional powers in \({\mathbb R}^{3}\) R 3 . The proof of the existence of solutions relies on a fixed point technique. Solvability conditions for the elliptic operators without the Fredholm property in unbounded domains are used.