Existence,uniqueness, and numerical approximations for stochastic Burgers equations |
| |
Authors: | Sara Mazzonetto Diyora Salimova |
| |
Institution: | 1. Institute of Mathematics, University of Potsdam, Potsdam, Germany;2. mazzonetto@uni-potsdam.de;4. Seminar for Applied Mathematics, ETH Zurich, Zurich, Switzerland |
| |
Abstract: | AbstractIn 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. |
| |
Keywords: | Stochastic Burgers equations SPDEs mild solution existence numerical approximation |
|
|