随机介质中燃烧的定量均匀化

IF 1.8 1区数学 Q1 MATHEMATICS, APPLIED Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-07-26 DOI:10.4171/aihpc/80

Y. Zhang, Andrej Zlatoš

{"title":"随机介质中燃烧的定量均匀化","authors":"Y. Zhang, Andrej Zlatoš","doi":"10.4171/aihpc/80","DOIUrl":null,"url":null,"abstract":"We obtain the first quantitative stochastic homogenization result for reaction-diffusion equations, for ignition reactions in dimensions $d\\le 3$ that either have finite ranges of dependence or are close enough to such reactions, and for solutions with initial data that approximate characteristic functions of general convex sets. We show algebraic rate of convergence of these solutions to their homogenized limits, which are (discontinuous) viscosity solutions of certain related Hamilton-Jacobi equations.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2021-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Quantitative homogenization for combustion in random media\",\"authors\":\"Y. Zhang, Andrej Zlatoš\",\"doi\":\"10.4171/aihpc/80\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We obtain the first quantitative stochastic homogenization result for reaction-diffusion equations, for ignition reactions in dimensions $d\\\\le 3$ that either have finite ranges of dependence or are close enough to such reactions, and for solutions with initial data that approximate characteristic functions of general convex sets. We show algebraic rate of convergence of these solutions to their homogenized limits, which are (discontinuous) viscosity solutions of certain related Hamilton-Jacobi equations.\",\"PeriodicalId\":55514,\"journal\":{\"name\":\"Annales De L Institut Henri Poincare-Analyse Non Lineaire\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2021-07-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"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/80\",\"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/80","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 2

摘要

我们获得了反应-扩散方程的第一个定量随机均匀化结果，对于具有有限依赖范围或足够接近此类反应的维数$d\le 3$的点火反应，以及具有近似一般凸集特征函数的初始数据的解。我们展示了这些解收敛到它们的均匀极限的代数速率，这是某些相关的Hamilton-Jacobi方程的(不连续)粘性解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Quantitative homogenization for combustion in random media

We obtain the first quantitative stochastic homogenization result for reaction-diffusion equations, for ignition reactions in dimensions $d\le 3$ that either have finite ranges of dependence or are close enough to such reactions, and for solutions with initial data that approximate characteristic functions of general convex sets. We show algebraic rate of convergence of these solutions to their homogenized limits, which are (discontinuous) viscosity solutions of certain related Hamilton-Jacobi equations.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Annales De L Institut Henri Poincare-Analyse Non Lineaire 数学-应用数学

CiteScore

4.10

自引率

5.30%

发文量

审稿时长

>12 weeks

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.