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

School of Mathematics and Statistics

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

27 Citations (Scopus)

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.

Original language	English
Pages (from-to)	324-367
Number of pages	44
Journal	Annals of Applied Probability
Volume	30
Issue number	1
DOIs	https://doi.org/10.1214/19-AAP1503
Publication status	Published - Feb 2020

Keywords

First-order conservation laws
Kinetic solution
Large deviations
Weak convergence approach

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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.",

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KW - Weak convergence approach

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

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Keywords

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