模糊q-最接近配准模型

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-06-24 DOI:10.1088/1361-6544/ad5781

Piotr B Mucha and Jan Peszek

{"title":"模糊q-最接近配准模型","authors":"Piotr B Mucha and Jan Peszek","doi":"10.1088/1361-6544/ad5781","DOIUrl":null,"url":null,"abstract":"The paper examines the issue of well-posedness of the Cucker-Smale model with communication restricted to the q-closest neighbors, known also as the Cucker-Dong model. With agents oscillating on the boundary of different clusters, the system becomes difficult to precisely define, which leads to further problems with kinetic limits as the number of agents tends to infinity. We introduce the fuzzy q-closest system, which circumvents the issues with well-posedness. For such a system we prove a stability estimate for measure-valued solutions and perform the kinetic mean-field limit.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"38 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A fuzzy q-closest alignment model\",\"authors\":\"Piotr B Mucha and Jan Peszek\",\"doi\":\"10.1088/1361-6544/ad5781\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper examines the issue of well-posedness of the Cucker-Smale model with communication restricted to the q-closest neighbors, known also as the Cucker-Dong model. With agents oscillating on the boundary of different clusters, the system becomes difficult to precisely define, which leads to further problems with kinetic limits as the number of agents tends to infinity. We introduce the fuzzy q-closest system, which circumvents the issues with well-posedness. For such a system we prove a stability estimate for measure-valued solutions and perform the kinetic mean-field limit.\",\"PeriodicalId\":54715,\"journal\":{\"name\":\"Nonlinearity\",\"volume\":\"38 1\",\"pages\":\"\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2024-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinearity\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1088/1361-6544/ad5781\",\"RegionNum\":2,\"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":"Nonlinearity","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1088/1361-6544/ad5781","RegionNum":2,"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

本文研究了卡克-斯马尔模型（Cucker-Smale model）的良好拟合问题，该模型的通信仅限于 q 个最接近的邻居，也称为卡克-董模型（Cucker-Dong model）。由于代理人在不同簇的边界上摆动，该系统变得难以精确定义，当代理人的数量趋于无穷大时，会进一步导致动力学极限问题。我们引入了模糊 q-closest 系统，它规避了问题的好拟性。对于这种系统，我们证明了量值解的稳定性估计，并进行了动力学均场极限。

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

A fuzzy q-closest alignment model

The paper examines the issue of well-posedness of the Cucker-Smale model with communication restricted to the q-closest neighbors, known also as the Cucker-Dong model. With agents oscillating on the boundary of different clusters, the system becomes difficult to precisely define, which leads to further problems with kinetic limits as the number of agents tends to infinity. We introduce the fuzzy q-closest system, which circumvents the issues with well-posedness. For such a system we prove a stability estimate for measure-valued solutions and perform the kinetic mean-field limit.

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

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.