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<p>We study the limit behavior of Cahn–Hilliard-type functionals in which the derivative is replaced by higher-order fractional derivatives and modulated by an oscillating factor. Depending on the ratio between the oscillation scale and the interface length, we identify three different regimes and prove <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Γ</mi> </math></EquationSource> </InlineEquation>-convergence in each regime to a suitable sharp-interface limit functional. In the extreme regimes, we prove a separation-of-scales effect that enables us to highlight the difference relative to the local models.</p>

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Homogenization in one-dimensional higher-order non-local models of phase transitions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月25日

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  • Fabrizio Caragiulo,
  • Sergio Scalabrino,
  • Edoardo Voglino

摘要

We study the limit behavior of Cahn–Hilliard-type functionals in which the derivative is replaced by higher-order fractional derivatives and modulated by an oscillating factor. Depending on the ratio between the oscillation scale and the interface length, we identify three different regimes and prove \(\Gamma \) Γ -convergence in each regime to a suitable sharp-interface limit functional. In the extreme regimes, we prove a separation-of-scales effect that enables us to highlight the difference relative to the local models.