Large deviation principles for first-order scalar conservation laws with stochastic forcing

Zhao Dong; Jiang Lun Wu; Rangrang Zhang; Tusheng Zhang

doi:10.1214/19-AAP1503

Large deviation principles for first-order scalar conservation laws with stochastic forcing

Zhao Dong, Jiang Lun Wu, Rangrang Zhang, Tusheng Zhang

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

27 引用（Scopus）

摘要

In this paper, we established the Freidlin-Wentzell-type large deviation principles for first-order scalar conservation laws perturbed by small multiplicative noise. Due to the lack of the viscous terms in the stochastic equations, the kinetic solution to the Cauchy problem for these first-order conservation laws is studied. Then, based on the well-posedness of the kinetic solutions, we show that the large deviations holds by utilising the weak convergence approach.

源语言	英语
页（从-至）	324-367
页数	44
期刊	Annals of Applied Probability
卷	30
期	1
DOI	https://doi.org/10.1214/19-AAP1503
出版状态	已出版 - 2月 2020

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Dong, Z., Wu, J. L., Zhang, R., & Zhang, T. (2020). Large deviation principles for first-order scalar conservation laws with stochastic forcing. Annals of Applied Probability, 30(1), 324-367. https://doi.org/10.1214/19-AAP1503

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abstract = "In this paper, we established the Freidlin-Wentzell-type large deviation principles for first-order scalar conservation laws perturbed by small multiplicative noise. Due to the lack of the viscous terms in the stochastic equations, the kinetic solution to the Cauchy problem for these first-order conservation laws is studied. Then, based on the well-posedness of the kinetic solutions, we show that the large deviations holds by utilising the weak convergence approach.",

keywords = "First-order conservation laws, Kinetic solution, Large deviations, Weak convergence approach",

author = "Zhao Dong and Wu, {Jiang Lun} and Rangrang Zhang and Tusheng Zhang",

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AU - Zhang, Rangrang

AU - Zhang, Tusheng

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N2 - In this paper, we established the Freidlin-Wentzell-type large deviation principles for first-order scalar conservation laws perturbed by small multiplicative noise. Due to the lack of the viscous terms in the stochastic equations, the kinetic solution to the Cauchy problem for these first-order conservation laws is studied. Then, based on the well-posedness of the kinetic solutions, we show that the large deviations holds by utilising the weak convergence approach.

AB - In this paper, we established the Freidlin-Wentzell-type large deviation principles for first-order scalar conservation laws perturbed by small multiplicative noise. Due to the lack of the viscous terms in the stochastic equations, the kinetic solution to the Cauchy problem for these first-order conservation laws is studied. Then, based on the well-posedness of the kinetic solutions, we show that the large deviations holds by utilising the weak convergence approach.

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Large deviation principles for first-order scalar conservation laws with stochastic forcing

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