Existence, uniqueness, and numerical approximations for stochastic Burgers equations

Authors

Sara Mazzonetto and Diyora Salimova

Reference

Stochastic Analysis and Applications, Vol. 38, No. 4, pp. 623-646, Jan. 2020.

DOI: 10.1080/07362994.2019.1709503

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.

Keywords

Stochastic Burgers equations, SPDEs, mild solution, existence, numerical approximation

Download this document:

This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.