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Heterogeneous stochastic scalar conservation laws with non-homogeneous Dirichlet boundary conditions

Guangying Lv, Jiang-lun Wu Orcid Logo

Journal of Hyperbolic Differential Equations, Volume: 15, Issue: 02, Pages: 291 - 328

Swansea University Author: Jiang-lun Wu Orcid Logo

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DOI (Published version): 10.1142/S021989161850011X

Abstract

We introduce a notion of stochastic entropy solutions for heterogeneous scalar conservation laws with multiplicative noise on a bounded domain with non-homogeneous boundary condition. Using the concept of measure-valued solutions and Kruzhkov's semi-entropy formulations, we show the existence a...

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Published in: Journal of Hyperbolic Differential Equations
ISBN: 1793-6993
ISSN: 0219-8916 1793-6993
Published: Singapore World Scientific 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa38288
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first_indexed 2018-01-24T19:56:14Z
last_indexed 2018-08-01T19:33:21Z
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spelling 2018-08-01T14:55:19.8590007 v2 38288 2018-01-24 Heterogeneous stochastic scalar conservation laws with non-homogeneous Dirichlet boundary conditions dbd67e30d59b0f32592b15b5705af885 0000-0003-4568-7013 Jiang-lun Wu Jiang-lun Wu true false 2018-01-24 SMA We introduce a notion of stochastic entropy solutions for heterogeneous scalar conservation laws with multiplicative noise on a bounded domain with non-homogeneous boundary condition. Using the concept of measure-valued solutions and Kruzhkov's semi-entropy formulations, we show the existence and uniqueness of stochastic entropy solutions. Moreover, we establish an explicit estimate for the continuous dependence of stochastic entropy solutions on the flux function and the random source function. Journal Article Journal of Hyperbolic Differential Equations 15 02 291 328 World Scientific Singapore 1793-6993 0219-8916 1793-6993 Scalar conservation law; entropy solutions; It\^{o}&apos;s formula. 21 6 2018 2018-06-21 10.1142/S021989161850011X COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2018-08-01T14:55:19.8590007 2018-01-24T15:44:37.2760667 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Guangying Lv 1 Jiang-lun Wu 0000-0003-4568-7013 2 0038288-24012018154535.pdf LvWu.pdf 2018-01-24T15:45:35.6070000 Output 341392 application/pdf Accepted Manuscript true 2019-06-21T00:00:00.0000000 12 month embargo. true eng
title Heterogeneous stochastic scalar conservation laws with non-homogeneous Dirichlet boundary conditions
spellingShingle Heterogeneous stochastic scalar conservation laws with non-homogeneous Dirichlet boundary conditions
Jiang-lun Wu
title_short Heterogeneous stochastic scalar conservation laws with non-homogeneous Dirichlet boundary conditions
title_full Heterogeneous stochastic scalar conservation laws with non-homogeneous Dirichlet boundary conditions
title_fullStr Heterogeneous stochastic scalar conservation laws with non-homogeneous Dirichlet boundary conditions
title_full_unstemmed Heterogeneous stochastic scalar conservation laws with non-homogeneous Dirichlet boundary conditions
title_sort Heterogeneous stochastic scalar conservation laws with non-homogeneous Dirichlet boundary conditions
author_id_str_mv dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Jiang-lun Wu
author2 Guangying Lv
Jiang-lun Wu
format Journal article
container_title Journal of Hyperbolic Differential Equations
container_volume 15
container_issue 02
container_start_page 291
publishDate 2018
institution Swansea University
isbn 1793-6993
issn 0219-8916
1793-6993
doi_str_mv 10.1142/S021989161850011X
publisher World Scientific
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description We introduce a notion of stochastic entropy solutions for heterogeneous scalar conservation laws with multiplicative noise on a bounded domain with non-homogeneous boundary condition. Using the concept of measure-valued solutions and Kruzhkov's semi-entropy formulations, we show the existence and uniqueness of stochastic entropy solutions. Moreover, we establish an explicit estimate for the continuous dependence of stochastic entropy solutions on the flux function and the random source function.
published_date 2018-06-21T03:48:25Z
_version_ 1763752337832148992
score 11.012678

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