Homogenization in one-dimensional higher-order non-local models of phase transitions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910253159809024 |
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| author | Caragiulo, Fabrizio Scalabrino, Sergio Voglino, Edoardo |
| author_facet | Caragiulo, Fabrizio Scalabrino, Sergio Voglino, Edoardo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12689 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Homogenization in one-dimensional higher-order non-local models of phase transitions Caragiulo, Fabrizio Scalabrino, Sergio Voglino, Edoardo Analysis of PDEs 49J45, 65K10 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. |
| title | Homogenization in one-dimensional higher-order non-local models of phase transitions |
| topic | Analysis of PDEs 49J45, 65K10 |
| url | https://arxiv.org/abs/2604.12689 |