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1. The Allen–Cahn equation with generic initial datum.

Author

Hairer, Martin, Lê, Khoa, and Rosati, Tommaso

Subjects
*EQUATIONS, *WHITE noise, *CURVATURE
Abstract

We consider the Allen–Cahn equation ∂ t u - Δ 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. [ABSTRACT FROM AUTHOR]

Published
2023
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