{"title":"Thin film equations with nonlinear deterministic and stochastic perturbations","authors":"Oleksiy Kapustyan , Olha Martynyuk , Oleksandr Misiats , Oleksandr Stanzhytskyi","doi":"10.1016/j.na.2024.113646","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we consider stochastic thin-film equation with nonlinear drift terms, colored Gaussian Stratonovich 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.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"250 ","pages":"Article 113646"},"PeriodicalIF":1.3000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0362546X24001652/pdfft?md5=f3d21fbe23f0caa335b0a9f697a81c70&pid=1-s2.0-S0362546X24001652-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Theory Methods & Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0362546X24001652","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper we consider stochastic thin-film equation with nonlinear drift terms, colored Gaussian Stratonovich 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.
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