{"title":"非线性扩散-平流方程不可压缩极限的收敛速率","authors":"Noemi David, Tomasz Dkebiec, B. Perthame","doi":"10.4171/aihpc/53","DOIUrl":null,"url":null,"abstract":"The incompressible limit of nonlinear diffusion equations of porous medium type has attracted a lot of attention in recent years, due to its ability to link the weak formulation of cell-population models to free boundary problems of Hele-Shaw type. Although vast literature is available on this singular limit, little is known on the convergence rate of the solutions. In this work, we compute the convergence rate in a negative Sobolev norm and, upon interpolating with BV -uniform bounds, we deduce a convergence rate in appropriate Lebesgue spaces. 2010 Mathematics Subject Classification. 35K57; 35K65; 35Q92; 35B45;","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"17 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2021-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Convergence rate for the incompressible limit of nonlinear diffusion–advection equations\",\"authors\":\"Noemi David, Tomasz Dkebiec, B. Perthame\",\"doi\":\"10.4171/aihpc/53\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The incompressible limit of nonlinear diffusion equations of porous medium type has attracted a lot of attention in recent years, due to its ability to link the weak formulation of cell-population models to free boundary problems of Hele-Shaw type. Although vast literature is available on this singular limit, little is known on the convergence rate of the solutions. In this work, we compute the convergence rate in a negative Sobolev norm and, upon interpolating with BV -uniform bounds, we deduce a convergence rate in appropriate Lebesgue spaces. 2010 Mathematics Subject Classification. 35K57; 35K65; 35Q92; 35B45;\",\"PeriodicalId\":55514,\"journal\":{\"name\":\"Annales De L Institut Henri Poincare-Analyse Non Lineaire\",\"volume\":\"17 1\",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2021-08-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales De L Institut Henri Poincare-Analyse Non Lineaire\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/aihpc/53\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/aihpc/53","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Convergence rate for the incompressible limit of nonlinear diffusion–advection equations
The incompressible limit of nonlinear diffusion equations of porous medium type has attracted a lot of attention in recent years, due to its ability to link the weak formulation of cell-population models to free boundary problems of Hele-Shaw type. Although vast literature is available on this singular limit, little is known on the convergence rate of the solutions. In this work, we compute the convergence rate in a negative Sobolev norm and, upon interpolating with BV -uniform bounds, we deduce a convergence rate in appropriate Lebesgue spaces. 2010 Mathematics Subject Classification. 35K57; 35K65; 35Q92; 35B45;
期刊介绍:
The Nonlinear Analysis section of the Annales de l''Institut Henri Poincaré is an international journal created in 1983 which publishes original and high quality research articles. It concentrates on all domains concerned with nonlinear analysis, specially applicable to PDE, mechanics, physics, economy, without overlooking the numerical aspects.