{"title":"Stability of planar rarefaction waves for scalar viscous conservation law under periodic perturbations","authors":"F. Huang, Qian Yuan","doi":"10.4310/maa.2021.v28.n3.a6","DOIUrl":null,"url":null,"abstract":"Abstract. The large time behavior of the solutions to a multi-dimensional viscous conservation law is considered in this paper. It is shown that the solution timeasymptotically tends to the planar rarefaction wave if the initial perturbations are multi-dimensional periodic. The time-decay rate is also obtained. Moreover, a Gagliardo-Nirenberg type inequality is established in the domain RˆTn ́1pn ě 2q, where Tn ́1 is the n ́ 1-dimensional torus.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2021-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"16","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Methods and applications of analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/maa.2021.v28.n3.a6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 16
Abstract
Abstract. The large time behavior of the solutions to a multi-dimensional viscous conservation law is considered in this paper. It is shown that the solution timeasymptotically tends to the planar rarefaction wave if the initial perturbations are multi-dimensional periodic. The time-decay rate is also obtained. Moreover, a Gagliardo-Nirenberg type inequality is established in the domain RˆTn ́1pn ě 2q, where Tn ́1 is the n ́ 1-dimensional torus.
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