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The stochastic thin-film equation: Existence of nonnegative martingale solutions

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  • Gess, Benjamin
  • Gnann, Manuel V.

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.

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  • Gess, Benjamin & Gnann, Manuel V., 2020. "The stochastic thin-film equation: Existence of nonnegative martingale solutions," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7260-7302.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:12:p:7260-7302
    DOI: 10.1016/j.spa.2020.07.013
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    References listed on IDEAS

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    1. Govindan, T.E., 2015. "On Trotter–Kato approximations of semilinear stochastic evolution equations in infinite dimensions," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 299-306.
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