{"title":"粘性消失极限下一维输运方程的均匀可控性","authors":"Camille Laurent, Matthieu Léautaud","doi":"10.5802/crmath.405","DOIUrl":null,"url":null,"abstract":"We consider a one dimensional transport equation with varying vector field and a small viscosity coefficient, controlled by one endpoint of the interval. We give upper and lower bounds on the minimal time needed to control to zero, uniformly in the vanishing viscosity limit.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":"45 1","pages":"0"},"PeriodicalIF":0.8000,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"On uniform controllability of 1D transport equations in the vanishing viscosity limit\",\"authors\":\"Camille Laurent, Matthieu Léautaud\",\"doi\":\"10.5802/crmath.405\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a one dimensional transport equation with varying vector field and a small viscosity coefficient, controlled by one endpoint of the interval. We give upper and lower bounds on the minimal time needed to control to zero, uniformly in the vanishing viscosity limit.\",\"PeriodicalId\":10620,\"journal\":{\"name\":\"Comptes Rendus Mathematique\",\"volume\":\"45 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-01-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus Mathematique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5802/crmath.405\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus Mathematique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/crmath.405","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
On uniform controllability of 1D transport equations in the vanishing viscosity limit
We consider a one dimensional transport equation with varying vector field and a small viscosity coefficient, controlled by one endpoint of the interval. We give upper and lower bounds on the minimal time needed to control to zero, uniformly in the vanishing viscosity limit.
期刊介绍：
The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, …
Articles are original notes that briefly describe an important discovery or result. The articles are written in French or English.
The journal also publishes review papers, thematic issues and texts reflecting the activity of Académie des sciences in the field of Mathematics.
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