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

Zhao Dong, Jiang-lun Wu Orcid Logo, Rangrang Zhang, Tusheng Zhang

The Annals of Applied Probability, Volume: 30, Issue: 1, Pages: 324 - 367

Swansea University Author: Jiang-lun Wu Orcid Logo

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DOI (Published version): 10.1214/19-aap1503

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: The Annals of Applied Probability
ISSN: 1050-5164 2168-8737
Published: Institute of Mathematical Statistics Institute of Mathematical Statistics 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa48584
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first_indexed 2019-01-28T20:02:35Z
last_indexed 2020-07-10T03:09:23Z
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spelling 2020-07-09T20:48:38.3780994 v2 48584 2019-01-28 Large deviation principles for first-order scalar conservation laws with stochastic forcing dbd67e30d59b0f32592b15b5705af885 0000-0003-4568-7013 Jiang-lun Wu Jiang-lun Wu true false 2019-01-28 SMA 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. Journal Article The Annals of Applied Probability 30 1 324 367 Institute of Mathematical Statistics Institute of Mathematical Statistics 1050-5164 2168-8737 large deviations; first-order conservation laws; weak convergence approach; kinetic solution. 25 2 2020 2020-02-25 10.1214/19-aap1503 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2020-07-09T20:48:38.3780994 2019-01-28T15:12:28.7540646 Zhao Dong 1 Jiang-lun Wu 0000-0003-4568-7013 2 Rangrang Zhang 3 Tusheng Zhang 4 48584__14058__cbfd09b1e37542ffb82e79bb33c8e7ac.pdf DWZZ2019-0129.pdf 2019-05-29T18:23:25.4700000 Output 251929 application/pdf Accepted Manuscript true 2019-05-29T00:00:00.0000000 true eng
title Large deviation principles for first-order scalar conservation laws with stochastic forcing
spellingShingle Large deviation principles for first-order scalar conservation laws with stochastic forcing
Jiang-lun Wu
title_short Large deviation principles for first-order scalar conservation laws with stochastic forcing
title_full Large deviation principles for first-order scalar conservation laws with stochastic forcing
title_fullStr Large deviation principles for first-order scalar conservation laws with stochastic forcing
title_full_unstemmed Large deviation principles for first-order scalar conservation laws with stochastic forcing
title_sort Large deviation principles for first-order scalar conservation laws with stochastic forcing
author_id_str_mv dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Jiang-lun Wu
author2 Zhao Dong
Jiang-lun Wu
Rangrang Zhang
Tusheng Zhang
format Journal article
container_title The Annals of Applied Probability
container_volume 30
container_issue 1
container_start_page 324
publishDate 2020
institution Swansea University
issn 1050-5164
2168-8737
doi_str_mv 10.1214/19-aap1503
publisher Institute of Mathematical Statistics
document_store_str 1
active_str 0
description 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.
published_date 2020-02-25T03:59:07Z
_version_ 1763753010967609344
score 11.036706

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