Tightness for a stochastic Allen–Cahn equation

Matthias Röger; Hendrik Weber

doi:10.1007/s40072-013-0004-4

Tightness for a stochastic Allen–Cahn equation

Matthias Röger
, Hendrik Weber

Department of Mathematical Sciences

Technische Universität Dortmund
University of Warwick

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

20 Citations (SciVal)

Abstract

We study an Allen–Cahn equation perturbed by a multiplicative stochastic noise that is white in time and correlated in space. Formally this equation approximates a stochastically forced mean curvature flow. We derive a uniform bound for the diffuse surface area, prove the tightness of solutions in the sharp interface limit, and show the convergence to phase-indicator functions.

Original language	English
Pages (from-to)	175-203
Journal	Stochastic Partial Differential Equations: Analysis and Computations
Volume	1
Issue number	1
DOIs	https://doi.org/10.1007/s40072-013-0004-4
Publication status	Published - 1 Mar 2013

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http://link.springer.com/10.1007/s40072-013-0004-4

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AB - We study an Allen–Cahn equation perturbed by a multiplicative stochastic noise that is white in time and correlated in space. Formally this equation approximates a stochastically forced mean curvature flow. We derive a uniform bound for the diffuse surface area, prove the tightness of solutions in the sharp interface limit, and show the convergence to phase-indicator functions.

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DO - 10.1007/s40072-013-0004-4

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JO - Stochastic Partial Differential Equations: Analysis and Computations

JF - Stochastic Partial Differential Equations: Analysis and Computations

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Tightness for a stochastic Allen–Cahn equation

Abstract

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