Sharp interface limit for $1$D stochastic Allen-Cahn equation in full small noise regime
| Title: | Sharp interface limit for $1$D stochastic Allen-Cahn equation in full small noise regime |
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| Authors: | Xu, Weijun, Zhao, Wenhao, Zhou, Shuhan |
| Publication Year: | 2024 |
| Collection: | Mathematics |
| Subject Terms: | Mathematics - Probability, Mathematics - Analysis of PDEs |
| More Details: | We study the sharp interface limit for the $1$D stochastic Allen-Cahn equation, and extend earlier work by Funaki to the full small noise regime. The main new idea is the construction of a series of functional correctors, which are designed to recursively cancel potential divergences. In addition, in order to show these correctors are well-behaved, we develop a systematic decomposition of functional derivatives of the deterministic Allen-Cahn flow of all orders. This decomposition is of its own interest, and may be useful in other situations as well. |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2402.19070 |
| Accession Number: | edsarx.2402.19070 |
| Database: | arXiv |
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