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.
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| Author details: | Sara MazzonettoORCiDGND, Diyora SalimovaORCiDGND |
|---|---|
| URN: | urn:nbn:de:kobv:517-opus4-515796 |
| DOI: | https://doi.org/10.25932/publishup-51579 |
| ISSN: | 1866-8372 |
| Title of parent work (German): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe |
| Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (1393) |
| Publication type: | Postprint |
| Language: | English |
| Date of first publication: | 2020/01/20 |
| Publication year: | 2020 |
| Publishing institution: | Universität Potsdam |
| Release date: | 2024/03/15 |
| Tag: | SPDEs; existence; mild solution; numerical approximation; stochastic Burgers equations |
| Issue: | 4 |
| Number of pages: | 26 |
| Source: | Stochastic Analysis and Applications, 38:4, 623-646, DOI: 10.1080/07362994.2019.1709503 |
| 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 / Green Open-Access |
| License (German): |  CC-BY-NC-ND - Namensnennung, nicht kommerziell, keine Bearbeitungen 4.0 International |
| External remark: | Bibliographieeintrag der Originalveröffentlichung/Quelle |
