具有一般初始数据的三尺度双曲型偏微分方程组的一致存在性和收敛性定理

IF 2.1 2区数学 Q1 MATHEMATICS

Communications in Partial Differential Equations Pub Date : 2022-10-25 DOI:10.1080/03605302.2022.2129383

S. Schochet, Xin Xu

{"title":"具有一般初始数据的三尺度双曲型偏微分方程组的一致存在性和收敛性定理","authors":"S. Schochet, Xin Xu","doi":"10.1080/03605302.2022.2129383","DOIUrl":null,"url":null,"abstract":"Abstract Uniform existence of solutions to initial-value problems and convergence of appropriately filtered solutions are proven for a special class of three-scale singular limit equations, without any restriction on the initial data. The uniform existence is proven using a novel system of energy estimates. The convergence result is based on a detailed analysis of the fastest-scale oscillations, which unlike in two-scale systems have no explicit solution formula.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"47 1","pages":"2401 - 2443"},"PeriodicalIF":2.1000,"publicationDate":"2022-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Toward uniform existence and convergence theorems for three-scale systems of hyperbolic PDEs with general initial data\",\"authors\":\"S. Schochet, Xin Xu\",\"doi\":\"10.1080/03605302.2022.2129383\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Uniform existence of solutions to initial-value problems and convergence of appropriately filtered solutions are proven for a special class of three-scale singular limit equations, without any restriction on the initial data. The uniform existence is proven using a novel system of energy estimates. The convergence result is based on a detailed analysis of the fastest-scale oscillations, which unlike in two-scale systems have no explicit solution formula.\",\"PeriodicalId\":50657,\"journal\":{\"name\":\"Communications in Partial Differential Equations\",\"volume\":\"47 1\",\"pages\":\"2401 - 2443\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2022-10-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Partial Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/03605302.2022.2129383\",\"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/10.1080/03605302.2022.2129383","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: 1

摘要

摘要证明了一类特殊的三尺度奇异极限方程初值问题解的一致存在性和适当滤波解的收敛性，对初值没有任何限制。使用一个新的能量估计系统证明了一致存在性。收敛结果基于对最快尺度振荡的详细分析，这与两个尺度系统不同，没有明确的解公式。

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

Toward uniform existence and convergence theorems for three-scale systems of hyperbolic PDEs with general initial data

Abstract Uniform existence of solutions to initial-value problems and convergence of appropriately filtered solutions are proven for a special class of three-scale singular limit equations, without any restriction on the initial data. The uniform existence is proven using a novel system of energy estimates. The convergence result is based on a detailed analysis of the fastest-scale oscillations, which unlike in two-scale systems have no explicit solution formula.

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.