Existence, uniqueness, and numerical approximations for stochastic Burgers equations

Open access
Date
2020Type
- Journal Article
Abstract
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. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000396003Publication status
publishedExternal links
Journal / series
Stochastic Analysis and ApplicationsVolume
Pages / Article No.
Publisher
Taylor & FrancisSubject
Stochastic Burgers equations; SPDEs; mild solution; existence; numerical approximationOrganisational unit
02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
03951 - Jentzen, Arnulf (ehemalig) / Jentzen, Arnulf (former)
Funding
175699 - Higher order numerical approximation methods for stochastic partial differential equations (SNF)
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