{"title":"周期扰动下标量粘性守恒定律平面稀疏波的稳定性","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":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"16","resultStr":"{\"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\":\" \",\"pages\":\"\"},\"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}","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}
Stability of planar rarefaction waves for scalar viscous conservation law under periodic perturbations
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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