Convergence Rate for Galerkin Approximation of the Stochastic Allen—Cahn Equations on 2D Torus

Ting Ma; Rong Chan Zhu

doi:10.1007/s10114-020-9367-4

Convergence Rate for Galerkin Approximation of the Stochastic Allen—Cahn Equations on 2D Torus

Ting Ma
, Rong Chan Zhu^*

^*此作品的通讯作者

数学学院

Sichuan University
Bielefeld University

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

In this paper we discuss the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations driven by space-time white noise on T². First we prove that the convergence rate for stochastic 2D heat equation is of order α — δ in Besov space C⁻^α for α ∈ (0,1) and δ > 0 arbitrarily small. Then we obtain the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations of order α — δ in C⁻^α for α ∈ (0,2/9) and δ > 0 arbitrarily small.

源语言	英语
页（从-至）	471-490
页数	20
期刊	Acta Mathematica Sinica, English Series
卷	37
期	3
DOI	https://doi.org/10.1007/s10114-020-9367-4
出版状态	已出版 - 3月 2021

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title = "Convergence Rate for Galerkin Approximation of the Stochastic Allen—Cahn Equations on 2D Torus",

abstract = "In this paper we discuss the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations driven by space-time white noise on T2. First we prove that the convergence rate for stochastic 2D heat equation is of order α — δ in Besov space C−α for α ∈ (0,1) and δ > 0 arbitrarily small. Then we obtain the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations of order α — δ in C−α for α ∈ (0,2/9) and δ > 0 arbitrarily small.",

keywords = "60H15, 82C28, Besov space, Galerkin projection, Stochastic Allen-Cahn equations, convergence rate, white noise",

author = "Ting Ma and Zhu, \{Rong Chan\}",

note = "Publisher Copyright: {\textcopyright} 2020, Springer-Verlag GmbH Germany \& The Editorial Office of AMS.",

year = "2021",

month = mar,

doi = "10.1007/s10114-020-9367-4",

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T1 - Convergence Rate for Galerkin Approximation of the Stochastic Allen—Cahn Equations on 2D Torus

AU - Ma, Ting

AU - Zhu, Rong Chan

PY - 2021/3

Y1 - 2021/3

N2 - In this paper we discuss the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations driven by space-time white noise on T2. First we prove that the convergence rate for stochastic 2D heat equation is of order α — δ in Besov space C−α for α ∈ (0,1) and δ > 0 arbitrarily small. Then we obtain the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations of order α — δ in C−α for α ∈ (0,2/9) and δ > 0 arbitrarily small.

AB - In this paper we discuss the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations driven by space-time white noise on T2. First we prove that the convergence rate for stochastic 2D heat equation is of order α — δ in Besov space C−α for α ∈ (0,1) and δ > 0 arbitrarily small. Then we obtain the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations of order α — δ in C−α for α ∈ (0,2/9) and δ > 0 arbitrarily small.

KW - 60H15

KW - 82C28

KW - Besov space

KW - Galerkin projection

KW - Stochastic Allen-Cahn equations

KW - convergence rate

KW - white noise

UR - https://www.scopus.com/pages/publications/85083802198

U2 - 10.1007/s10114-020-9367-4

DO - 10.1007/s10114-020-9367-4

M3 - Article

AN - SCOPUS:85083802198

SN - 1439-8516

VL - 37

SP - 471

EP - 490

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 3

ER -

Convergence Rate for Galerkin Approximation of the Stochastic Allen—Cahn Equations on 2D Torus

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