关于具有非均匀外部约束的更新方程的均化

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Acta Applicandae Mathematicae Pub Date : 2023-08-30 DOI:10.1007/s10440-023-00594-2

Étienne Bernard, Francesco Salvarani

{"title":"关于具有非均匀外部约束的更新方程的均化","authors":"Étienne Bernard, Francesco Salvarani","doi":"10.1007/s10440-023-00594-2","DOIUrl":null,"url":null,"abstract":"<div><p>We study the homogenization limit of the renewal equation with heterogeneous external constraints by means of the two-scale convergence theory. We prove that the homogenized limit satisfies an equation involving non-local terms, which are the consequence of the oscillations in the birth and death terms. We have moreover shown that the numerical approximation of the homogenized equation via the two-scale limit gives an alternative way for the numerical study of the solution of the limiting problem.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-023-00594-2.pdf","citationCount":"0","resultStr":"{\"title\":\"On the Homogenization of the Renewal Equation with Heterogeneous External Constraints\",\"authors\":\"Étienne Bernard, Francesco Salvarani\",\"doi\":\"10.1007/s10440-023-00594-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study the homogenization limit of the renewal equation with heterogeneous external constraints by means of the two-scale convergence theory. We prove that the homogenized limit satisfies an equation involving non-local terms, which are the consequence of the oscillations in the birth and death terms. We have moreover shown that the numerical approximation of the homogenized equation via the two-scale limit gives an alternative way for the numerical study of the solution of the limiting problem.</p></div>\",\"PeriodicalId\":53132,\"journal\":{\"name\":\"Acta Applicandae Mathematicae\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10440-023-00594-2.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Applicandae Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10440-023-00594-2\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Applicandae Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10440-023-00594-2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

利用两尺度收敛理论研究了具有异质外部约束的更新方程的均匀化极限。我们证明了齐化极限满足一个包含非局部项的方程，这是出生项和死亡项振荡的结果。此外，我们还表明，通过两尺度极限对齐次方程进行数值逼近，为数值研究极限问题的解提供了一种替代方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On the Homogenization of the Renewal Equation with Heterogeneous External Constraints

查看原文本刊更多论文

On the Homogenization of the Renewal Equation with Heterogeneous External Constraints

We study the homogenization limit of the renewal equation with heterogeneous external constraints by means of the two-scale convergence theory. We prove that the homogenized limit satisfies an equation involving non-local terms, which are the consequence of the oscillations in the birth and death terms. We have moreover shown that the numerical approximation of the homogenized equation via the two-scale limit gives an alternative way for the numerical study of the solution of the limiting problem.

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

Acta Applicandae Mathematicae 数学-应用数学

CiteScore

2.80

自引率

6.20%

发文量

审稿时长

16.2 months

期刊介绍： Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods. Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.