TY - JOUR
T1 - The stochastic thin-film equation
T2 - Existence of nonnegative martingale solutions
AU - Gess, Benjamin
AU - Gnann, Manuel V.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85089194219&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2020.07.013
DO - 10.1016/j.spa.2020.07.013
M3 - Article
AN - SCOPUS:85089194219
SN - 0304-4149
VL - 130
SP - 7260
EP - 7302
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 12
ER -