Existence, uniqueness, and numerical approximations for stochastic burgers equations
- In this article, we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existing fully explicit space-time discrete approximation scheme, in particular the fact that it satisfies suitable a priori estimates. We also obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the article to the stochastic Burgers equations with additive space-time white noise.
| Author details: | Sara MazzonettoORCiDGND, Diyora SalimovaORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1080/07362994.2019.1709503 |
| ISSN: | 0736-2994 |
| ISSN: | 1532-9356 |
| Title of parent work (English): | Stochastic analysis and applications |
| Publisher: | Taylor & Francis Group |
| Place of publishing: | Philadelphia |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2020/01/20 |
| Publication year: | 2020 |
| Release date: | 2023/03/21 |
| Tag: | SPDEs; Stochastic Burgers equations; approximation; existence; mild solution; numerical |
| Volume: | 38 |
| Issue: | 4 |
| Number of pages: | 24 |
| First page: | 623 |
| Last Page: | 646 |
| Funding institution: | Deutsche Forschungsgesellschaft (DFG)German Research Foundation (DFG); [RTG 2131]; Swiss National Science Foundation (SNSF)Swiss National; Science Foundation (SNSF) [175699]; (Labex CEMPI) Center Europeen pour; les Mathematiques, la Physique et leurs interactions; [ANR-11-LABX-0007-01] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Hybrid Open-Access |
| License (German): |  CC-BY-NC-ND - Namensnennung, nicht kommerziell, keine Bearbeitungen 4.0 International |
| External remark: | Zweitveröffentlichung in der Schriftenreihe Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 1393 |
