{"title":"一类非线性高阶Kirchhoff方程的随机吸引子族的存在性","authors":"Guoguang Lin, C. Zhu","doi":"10.4236/IJMNTA.2019.82003","DOIUrl":null,"url":null,"abstract":"The existence of random attractor family for a class of nonlinear nonlocal higher-order Kirchhoff partial differential equations with additive white noise is studied. The weak solution of the equation is established by the Ornstein-Uhlenbeck process to deal with the random term, and a bounded random absorption set is obtained. And then, the existence of the random attractor family is proved by the isomorphism mapping method.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Existence of Random Attractor Family for a Class of Nonlinear Higher-Order Kirchhoff Equations\",\"authors\":\"Guoguang Lin, C. Zhu\",\"doi\":\"10.4236/IJMNTA.2019.82003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The existence of random attractor family for a class of nonlinear nonlocal higher-order Kirchhoff partial differential equations with additive white noise is studied. The weak solution of the equation is established by the Ornstein-Uhlenbeck process to deal with the random term, and a bounded random absorption set is obtained. And then, the existence of the random attractor family is proved by the isomorphism mapping method.\",\"PeriodicalId\":69680,\"journal\":{\"name\":\"现代非线性理论与应用(英文)\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-04-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"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.2019.82003\",\"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.2019.82003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Existence of Random Attractor Family for a Class of Nonlinear Higher-Order Kirchhoff Equations
The existence of random attractor family for a class of nonlinear nonlocal higher-order Kirchhoff partial differential equations with additive white noise is studied. The weak solution of the equation is established by the Ornstein-Uhlenbeck process to deal with the random term, and a bounded random absorption set is obtained. And then, the existence of the random attractor family is proved by the isomorphism mapping method.
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