Hairer, M, Lê, K orcid.org/0000-0002-7654-7139 and Rosati, T (2023) The Allen–Cahn equation with generic initial datum. Probability Theory and Related Fields, 186. pp. 957-998. ISSN 0178-8051
Abstract
We consider the Allen–Cahn equation ∂tu−Δu=u−u3 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.
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Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Allen–Cahn equation; White noise; Mean curvature flow; Coarsening |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 21 Apr 2023 14:36 |
Last Modified: | 21 Jul 2023 10:25 |
Published Version: | https://link.springer.com/article/10.1007/s00440-0... |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s00440-023-01198-5 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:198431 |
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