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Large deviation principles for first-order scalar conservation laws with stochastic forcing / Zhao Dong; Jiang-Lun Wu; Rangrang Zhang; Tusheng Zhang

Annals of Applied Probability

Swansea University Author: Wu, Jiang-lun

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 co...

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Published in: Annals of Applied Probability
ISSN: 1050-5164 2168-8737
Published: The Institute of Mathematical Statistics
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa48584
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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 conser- vation 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: large deviations; first-order conservation laws; weak convergence approach; kinetic solution.
College: College of Science