{"title":"具有白噪声的高阶光束方程的随机吸引子族","authors":"Guoguang Lin, Jie Liu","doi":"10.4236/IJMNTA.2020.93004","DOIUrl":null,"url":null,"abstract":"In this paper, we studied a class of damped high order Beam equation stochas-tic dynamical systems with white noise. First, the Ornstein-Uhlenbeck process is used to transform the equation into a noiseless random equation with random variables as parameters. Secondly, by estimating the solution of the equation, we can obtain the bounded random absorption set. Finally, the isomorphism mapping method and compact embedding theorem are used to obtain the system. It is progressively compact, then we can prove the existence of ran-dom attractors.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Random Attractor Family of the High Order Beam Equations with White Noise\",\"authors\":\"Guoguang Lin, Jie Liu\",\"doi\":\"10.4236/IJMNTA.2020.93004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we studied a class of damped high order Beam equation stochas-tic dynamical systems with white noise. First, the Ornstein-Uhlenbeck process is used to transform the equation into a noiseless random equation with random variables as parameters. Secondly, by estimating the solution of the equation, we can obtain the bounded random absorption set. Finally, the isomorphism mapping method and compact embedding theorem are used to obtain the system. It is progressively compact, then we can prove the existence of ran-dom attractors.\",\"PeriodicalId\":69680,\"journal\":{\"name\":\"现代非线性理论与应用(英文)\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"现代非线性理论与应用(英文)\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://doi.org/10.4236/IJMNTA.2020.93004\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"现代非线性理论与应用(英文)","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.4236/IJMNTA.2020.93004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Random Attractor Family of the High Order Beam Equations with White Noise
In this paper, we studied a class of damped high order Beam equation stochas-tic dynamical systems with white noise. First, the Ornstein-Uhlenbeck process is used to transform the equation into a noiseless random equation with random variables as parameters. Secondly, by estimating the solution of the equation, we can obtain the bounded random absorption set. Finally, the isomorphism mapping method and compact embedding theorem are used to obtain the system. It is progressively compact, then we can prove the existence of ran-dom attractors.