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

par Caragiulo, Fabrizio ;Scalabrino, Sergio;Voglino, Edoardo
Référence Ricerche di Matematica
Publication Publié, 2026

Article révisé par les pairs

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Résumé :

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 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.