Homogenization in one-dimensional higher-order non-local models of phase transitions
Abstract
Abstract 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.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Solidification and crystal growth phenomena
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Ricerche di Matematica
- Publisher
- Springer Science and Business Media LLC
- Publication date
- 25 May 2026
- Language
- EN