Sharp Interface Limit of Stochastic Cahn-Hilliard Equation with Singular Noise

Ľubomír Baňas; Huanyu Yang; Rongchan Zhu

doi:10.1007/s11118-021-09976-3

Sharp Interface Limit of Stochastic Cahn-Hilliard Equation with Singular Noise

Ľubomír Baňas, Huanyu Yang^*, Rongchan Zhu

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We study the sharp interface limit of the two dimensional stochastic Cahn-Hilliard equation driven by two types of singular noise: a space-time white noise and a space-time singular divergence-type noise. We show that with appropriate scaling of the noise the solutions of the stochastic problems converge to the solutions of the determinisitic Mullins-Sekerka/Hele-Shaw problem.

Original language	English
Pages (from-to)	497-518
Number of pages	22
Journal	Potential Analysis
Volume	59
Issue number	2
DOIs	https://doi.org/10.1007/s11118-021-09976-3
Publication status	Published - Aug 2023

Keywords

Mullins-Sekerka/Hele-Shaw problem
Sharp interface limit
Singular noise
Stochastic Cahn-Hilliard equation

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10.1007/s11118-021-09976-3

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title = "Sharp Interface Limit of Stochastic Cahn-Hilliard Equation with Singular Noise",

abstract = "We study the sharp interface limit of the two dimensional stochastic Cahn-Hilliard equation driven by two types of singular noise: a space-time white noise and a space-time singular divergence-type noise. We show that with appropriate scaling of the noise the solutions of the stochastic problems converge to the solutions of the determinisitic Mullins-Sekerka/Hele-Shaw problem.",

keywords = "Mullins-Sekerka/Hele-Shaw problem, Sharp interface limit, Singular noise, Stochastic Cahn-Hilliard equation",

author = "{\v L}ubom{\'i}r Ba{\v n}as and Huanyu Yang and Rongchan Zhu",

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AU - Zhu, Rongchan

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N2 - We study the sharp interface limit of the two dimensional stochastic Cahn-Hilliard equation driven by two types of singular noise: a space-time white noise and a space-time singular divergence-type noise. We show that with appropriate scaling of the noise the solutions of the stochastic problems converge to the solutions of the determinisitic Mullins-Sekerka/Hele-Shaw problem.

AB - We study the sharp interface limit of the two dimensional stochastic Cahn-Hilliard equation driven by two types of singular noise: a space-time white noise and a space-time singular divergence-type noise. We show that with appropriate scaling of the noise the solutions of the stochastic problems converge to the solutions of the determinisitic Mullins-Sekerka/Hele-Shaw problem.

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KW - Sharp interface limit

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ER -

Sharp Interface Limit of Stochastic Cahn-Hilliard Equation with Singular Noise

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Keywords

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