Γ-Convergence and Stochastic Homogenization of Second-Order Singular Perturbation Models for Phase Transitions

Donnarumma AF (2025)


Publication Type: Journal article

Publication year: 2025

Journal

Book Volume: 35

Article Number: 14

Journal Issue: 1

DOI: 10.1007/s00332-024-10110-x

Abstract

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.

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How to cite

APA:

Donnarumma, A.F. (2025). Γ-Convergence and Stochastic Homogenization of Second-Order Singular Perturbation Models for Phase Transitions. Journal of Nonlinear Science, 35(1). https://doi.org/10.1007/s00332-024-10110-x

MLA:

Donnarumma, Antonio Flavio. "Γ-Convergence and Stochastic Homogenization of Second-Order Singular Perturbation Models for Phase Transitions." Journal of Nonlinear Science 35.1 (2025).

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