The Allen-Cahn equation with generic initial datum

Autor:	Hairer, Martin, Lê, Khoa, Rosati, Tommaso
Rok vydání:	2022
Předmět:	Mathematics - Analysis of PDEs Mathematics - Probability 60H15 35R60 53E10
Druh dokumentu:	Working Paper
Popis:	We consider the Allen-Cahn equation $\partial_t u- \Delta u=u-u^3$ with a rapidly mixing Gaussian field as initial condition. We show that provided that the amplitude of the initial condition is not too large, the equation generates fronts described by nodal sets of the Bargmann-Fock Gaussian field, which then evolve according to mean curvature flow.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2201.08426 Zobrazit plný text záznamu View this record from Arxiv