The stochastic thin-film equation

Existence of nonnegative martingale solutions

Journal article (2020)

Authors

Benjamin Gess Bielefeld University, Max Planck Institute
M.V. Gnann Analysis - EEMCS
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2020 Benjamin Gess, M.V. Gnann
DOI: https://doi.org/10.1016/j.spa.2020.07.013
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Published Date

2020

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

We consider the stochastic thin-film equation with colored Gaussian Stratonovich noise in one space dimension and establish the existence of nonnegative weak (martingale) solutions. The construction is based on a Trotter–Kato-type decomposition into a deterministic and a stochastic evolution, which yields an easy to implement numerical algorithm. Compared to previous work, no interface potential has to be included, the initial data and the solution can have de-wetted regions of positive measure, and the Trotter–Kato scheme allows for a simpler proof of existence than in case of Itô noise.