2024/06/20 by Antonio Flavio Donnarumma, Donnarumma, Antonio Flavio · 1 citation
Computer Science · Mathematics · #49J45 #49Q20 #60K35 #74E30 #74K15 #74Q05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2406.14356
openalex publication_date 2024/06/20 · openalex created_date 2024/06/22 · openalex updated_date 2026/07/28
We study the effective behavior of random, heterogeneous, anisotropic, second order phase transitions energies that arise in the study of pattern formations in physical-chemical systems. Specifically, we study the asymptotic behavior, as ε goes to zero, of random heterogeneous anisotropic functionals in which the second order perturbation competes not only with a double well potential but also with a possibly negative contribution given by the first order term. We prove that, under suitable growth conditions and under a stationarity assumption, the functionals Γ-converge almost surely to a surface energy whose density is independent of the space variable. Furthermore, we show that the limit surface density can be described via a suitable cell formula and is deterministic when ergodicity is assumed.