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On the regularity of weak solutions to space–time fractional stochastic heat equations

Guang-an Zou, Guangying Lv, Jiang-lun Wu

Statistics & Probability Letters, Volume: 139, Pages: 84 - 89

Swansea University Author: Jiang-lun Wu

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DOI (Published version): 10.1016/j.spl.2018.04.006

Abstract

This study is concerned with the space-time fractional stochastic heat-type equations driven by multiplicative noise, which can be used to model the anomalous heat diffusion in porous media with random effects with thermal memory. We first deduce the weak solutions to the given problem by means of t...

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Published in: Statistics & Probability Letters
ISSN: 01677152
Published: ELSEVIER 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa39293
first_indexed 2018-04-02T13:38:49Z
last_indexed 2018-05-15T12:34:03Z
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spelling 2018-05-15T10:59:26.5859380 v2 39293 2018-04-02 On the regularity of weak solutions to space–time fractional stochastic heat equations dbd67e30d59b0f32592b15b5705af885 Jiang-lun Wu Jiang-lun Wu true false 2018-04-02 This study is concerned with the space-time fractional stochastic heat-type equations driven by multiplicative noise, which can be used to model the anomalous heat diffusion in porous media with random effects with thermal memory. We first deduce the weak solutions to the given problem by means of the Laplace transform and Mittag-Leffler function. Using the fractional calculus and stochastic analysis theory, we further prove the pathwise spatial-temporal regularity properties of weak solutions to this type of SPDEs in the framework of Bochner spaces. Journal Article Statistics & Probability Letters 139 84 89 ELSEVIER 01677152 Space-time fractional derivative, stochastic heat equations, weak solutions, regularity properties. 31 8 2018 2018-08-31 10.1016/j.spl.2018.04.006 https://www.sciencedirect.com/science/article/pii/S0167715218301469 COLLEGE NANME COLLEGE CODE Swansea University 2018-05-15T10:59:26.5859380 2018-04-02T10:20:32.8038124 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Guang-an Zou 1 Guangying Lv 2 Jiang-lun Wu 3 0039293-02042018102124.pdf STFSE.pdf 2018-04-02T10:21:24.4400000 Output 255760 application/pdf Accepted Manuscript true 2019-04-14T00:00:00.0000000 12 month embargo. CC-BY-NC-ND. true eng
title On the regularity of weak solutions to space–time fractional stochastic heat equations
spellingShingle On the regularity of weak solutions to space–time fractional stochastic heat equations
Jiang-lun Wu
title_short On the regularity of weak solutions to space–time fractional stochastic heat equations
title_full On the regularity of weak solutions to space–time fractional stochastic heat equations
title_fullStr On the regularity of weak solutions to space–time fractional stochastic heat equations
title_full_unstemmed On the regularity of weak solutions to space–time fractional stochastic heat equations
title_sort On the regularity of weak solutions to space–time fractional stochastic heat equations
author_id_str_mv dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Jiang-lun Wu
author2 Guang-an Zou
Guangying Lv
Jiang-lun Wu
format Journal article
container_title Statistics & Probability Letters
container_volume 139
container_start_page 84
publishDate 2018
institution Swansea University
issn 01677152
doi_str_mv 10.1016/j.spl.2018.04.006
publisher ELSEVIER
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
url https://www.sciencedirect.com/science/article/pii/S0167715218301469
document_store_str 1
active_str 0
description This study is concerned with the space-time fractional stochastic heat-type equations driven by multiplicative noise, which can be used to model the anomalous heat diffusion in porous media with random effects with thermal memory. We first deduce the weak solutions to the given problem by means of the Laplace transform and Mittag-Leffler function. Using the fractional calculus and stochastic analysis theory, we further prove the pathwise spatial-temporal regularity properties of weak solutions to this type of SPDEs in the framework of Bochner spaces.
published_date 2018-08-31T19:22:43Z
_version_ 1821343967913967616
score 11.04748

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