具有全对全相互作用内核的欧拉型自组织系统弱解的无条件成群问题

IF 1.3 2区数学 Q1 MATHEMATICS Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-05-24 DOI:10.1016/j.na.2024.113576

Debora Amadori , Cleopatra Christoforou

{"title":"具有全对全相互作用内核的欧拉型自组织系统弱解的无条件成群问题","authors":"Debora Amadori , Cleopatra Christoforou","doi":"10.1016/j.na.2024.113576","DOIUrl":null,"url":null,"abstract":"<div><p>We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in one-space dimension and establish that the global entropy weak solutions, constructed in Amadori and Christoforou (2022) to the Cauchy problem for any <span><math><mrow><mi>B</mi><mi>V</mi></mrow></math></span> initial data that has finite total mass confined in a bounded interval and initial density uniformly positive therein, admit unconditional time-asymptotic flocking without any further assumptions on the initial data. In addition, we show that the convergence to a flocking profile occurs exponentially fast.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"245 ","pages":"Article 113576"},"PeriodicalIF":1.3000,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0362546X24000956/pdfft?md5=6a93db7ec31a9b1dcb1acab286d942f3&pid=1-s2.0-S0362546X24000956-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Unconditional flocking for weak solutions to self-organized systems of Euler-type with all-to-all interaction kernel\",\"authors\":\"Debora Amadori , Cleopatra Christoforou\",\"doi\":\"10.1016/j.na.2024.113576\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in one-space dimension and establish that the global entropy weak solutions, constructed in Amadori and Christoforou (2022) to the Cauchy problem for any <span><math><mrow><mi>B</mi><mi>V</mi></mrow></math></span> initial data that has finite total mass confined in a bounded interval and initial density uniformly positive therein, admit unconditional time-asymptotic flocking without any further assumptions on the initial data. In addition, we show that the convergence to a flocking profile occurs exponentially fast.</p></div>\",\"PeriodicalId\":49749,\"journal\":{\"name\":\"Nonlinear Analysis-Theory Methods & Applications\",\"volume\":\"245 \",\"pages\":\"Article 113576\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-05-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0362546X24000956/pdfft?md5=6a93db7ec31a9b1dcb1acab286d942f3&pid=1-s2.0-S0362546X24000956-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Analysis-Theory Methods & Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0362546X24000956\",\"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":"Nonlinear Analysis-Theory Methods & Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0362546X24000956","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: 0

摘要

我们考虑了一个在单空间维度上具有全对全相互作用核的成群结队型流体力学模型，并确定了 Amadori 和 Christoforou（2022 年）针对任何 BV 初始数据的考奇问题所构建的全局熵弱解，无需对初始数据做任何进一步假设，即可实现无条件的时间渐近成群结队。此外，我们还证明了成群曲线的收敛速度是指数级的。

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

Unconditional flocking for weak solutions to self-organized systems of Euler-type with all-to-all interaction kernel

We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in one-space dimension and establish that the global entropy weak solutions, constructed in Amadori and Christoforou (2022) to the Cauchy problem for any $B V$ initial data that has finite total mass confined in a bounded interval and initial density uniformly positive therein, admit unconditional time-asymptotic flocking without any further assumptions on the initial data. In addition, we show that the convergence to a flocking profile occurs exponentially fast.

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

Nonlinear Analysis-Theory Methods & Applications 数学-数学

CiteScore

3.30

自引率

0.00%

发文量

265

审稿时长

60 days

期刊介绍： Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.

期刊最新文献

Lie groups of real analytic diffeomorphisms are L1-regular Instability of the solitary wave solutions for the generalized derivative nonlinear Schrödinger equation in the endpoint case Examples of tangent cones of non-collapsed Ricci limit spaces A useful subdifferential in the Calculus of Variations Sobolev spaces for singular perturbation of 2D Laplace operator