Thin Film Equations with Nonlinear Deterministic and Stochastic Perturbations

TL;DR

This paper studies stochastic thin-film equations with nonlinear drift and noise, introducing a decomposition scheme that converges to a non-negative weak martingale solution, advancing understanding of such complex stochastic PDEs.

Contribution

It develops a Trotter-Kato-type decomposition scheme for nonlinear stochastic thin-film equations with colored noise, proving its convergence to a weak martingale solution.

Findings

Established convergence of the scheme to a non-negative weak martingale solution.

Extended the analysis to equations with nonlinear drift and colored Gaussian or Wiener noise.

Provided a framework for numerical approximation of complex stochastic PDEs.

Abstract

In this paper we consider stochastic thin-film equation with nonlinear drift terms, colored Gaussian Stratonovych noise, as well as nonlinear colored Wiener noise. By means of Trotter-Kato-type decomposition into deterministic and stochastic parts, we couple both of these dynamics via a discrete-in-time scheme, and establish its convergence to a non-negative weak martingale solution.