一类有缺陷的周期Hamilton-Jacobi方程的齐化

IF 2.1 2区数学 Q1 MATHEMATICS

Communications in Partial Differential Equations Pub Date : 2022-11-29 DOI:10.1080/03605302.2023.2238953

Y. Achdou, Claude Le Bris

{"title":"一类有缺陷的周期Hamilton-Jacobi方程的齐化","authors":"Y. Achdou, Claude Le Bris","doi":"10.1080/03605302.2023.2238953","DOIUrl":null,"url":null,"abstract":"Abstract We study homogenization for a class of stationary Hamilton-Jacobi equations in which the Hamiltonian is obtained by perturbing near the origin an otherwise periodic Hamiltonian. We prove that the limiting problem consists of a Hamilton-Jacobi equation outside the origin, with the same effective Hamiltonian as in periodic homogenization, supplemented at the origin with an effective Dirichlet condition that keeps track of the perturbation. Various comments and extensions are discussed.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"48 1","pages":"944 - 986"},"PeriodicalIF":2.1000,"publicationDate":"2022-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Homogenization of some periodic Hamilton-Jacobi equations with defects\",\"authors\":\"Y. Achdou, Claude Le Bris\",\"doi\":\"10.1080/03605302.2023.2238953\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We study homogenization for a class of stationary Hamilton-Jacobi equations in which the Hamiltonian is obtained by perturbing near the origin an otherwise periodic Hamiltonian. We prove that the limiting problem consists of a Hamilton-Jacobi equation outside the origin, with the same effective Hamiltonian as in periodic homogenization, supplemented at the origin with an effective Dirichlet condition that keeps track of the perturbation. Various comments and extensions are discussed.\",\"PeriodicalId\":50657,\"journal\":{\"name\":\"Communications in Partial Differential Equations\",\"volume\":\"48 1\",\"pages\":\"944 - 986\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2022-11-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Partial Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/03605302.2023.2238953\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Partial Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/03605302.2023.2238953","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 2

摘要

摘要研究了一类稳态Hamilton-Jacobi方程的齐次化问题，该类方程的哈密顿量是通过在原点附近的一个周期哈密顿量进行扰动得到的。我们证明了极限问题由原点外的哈密顿-雅可比方程组成，该方程具有与周期齐次化中相同的有效哈密顿量，并在原点处补充了跟踪扰动的有效狄利克雷条件。讨论了各种注释和扩展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Homogenization of some periodic Hamilton-Jacobi equations with defects

Abstract We study homogenization for a class of stationary Hamilton-Jacobi equations in which the Hamiltonian is obtained by perturbing near the origin an otherwise periodic Hamiltonian. We prove that the limiting problem consists of a Hamilton-Jacobi equation outside the origin, with the same effective Hamiltonian as in periodic homogenization, supplemented at the origin with an effective Dirichlet condition that keeps track of the perturbation. Various comments and extensions are discussed.

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

Communications in Partial Differential Equations 数学-数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal aims to publish high quality papers concerning any theoretical aspect of partial differential equations, as well as its applications to other areas of mathematics. Suitability of any paper is at the discretion of the editors. We seek to present the most significant advances in this central field to a wide readership which includes researchers and graduate students in mathematics and the more mathematical aspects of physics and engineering.