{"title":"光滑区域上多维Kuramoto-Sivashinsky方程的全局正则解","authors":"N. Larkin","doi":"10.47443/ejm.2022.015","DOIUrl":null,"url":null,"abstract":"Initial-boundary value problems for the $n$-dimensional ($n$ is a natural number from the interval [2,7]) Kuramoto-Sivashinsky equation posed on smooth bounded domains in $\\mathbb{R}^n$ were considered. The existence and uniqueness of global regular solutions as well as their exponential decay have been considered.","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"114 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Global regular solutions for the multi-dimensional Kuramoto-Sivashinsky equation posed on smooth domains\",\"authors\":\"N. Larkin\",\"doi\":\"10.47443/ejm.2022.015\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Initial-boundary value problems for the $n$-dimensional ($n$ is a natural number from the interval [2,7]) Kuramoto-Sivashinsky equation posed on smooth bounded domains in $\\\\mathbb{R}^n$ were considered. The existence and uniqueness of global regular solutions as well as their exponential decay have been considered.\",\"PeriodicalId\":29770,\"journal\":{\"name\":\"International Electronic Journal of Mathematics Education\",\"volume\":\"114 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2022-03-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Electronic Journal of Mathematics Education\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.47443/ejm.2022.015\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"EDUCATION & EDUCATIONAL RESEARCH\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Electronic Journal of Mathematics Education","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47443/ejm.2022.015","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"EDUCATION & EDUCATIONAL RESEARCH","Score":null,"Total":0}
Global regular solutions for the multi-dimensional Kuramoto-Sivashinsky equation posed on smooth domains
Initial-boundary value problems for the $n$-dimensional ($n$ is a natural number from the interval [2,7]) Kuramoto-Sivashinsky equation posed on smooth bounded domains in $\mathbb{R}^n$ were considered. The existence and uniqueness of global regular solutions as well as their exponential decay have been considered.
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