用新的拓扑性质的迭代方法来展示Burgers方程的一个新的经典解

IF 0.7 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2025-05-13 DOI:10.1007/s00010-025-01161-w

Svetlin G. Georgiev, Aissa Boukarou, Khaled Zennir, Keltoum Bouhali

{"title":"用新的拓扑性质的迭代方法来展示Burgers方程的一个新的经典解","authors":"Svetlin G. Georgiev, Aissa Boukarou, Khaled Zennir, Keltoum Bouhali","doi":"10.1007/s00010-025-01161-w","DOIUrl":null,"url":null,"abstract":"<div><p>Obtaining the classical solutions of quasi-linear differential equations is a complex mathematical problem usually solved by a limited number of mathematical techniques. Burgers’s equation is offered for modeling the dynamics of a viscous medium while studying the quantitative properties and classical solutions. An iterative method with new appropriate topological properties is presented to show one classical solution for the problem (1.1) and at least two non-negative classical solutions.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 4","pages":"1641 - 1655"},"PeriodicalIF":0.7000,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Iterative methods with new topological properties to show a new classical solutions of the Burgers equation\",\"authors\":\"Svetlin G. Georgiev, Aissa Boukarou, Khaled Zennir, Keltoum Bouhali\",\"doi\":\"10.1007/s00010-025-01161-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Obtaining the classical solutions of quasi-linear differential equations is a complex mathematical problem usually solved by a limited number of mathematical techniques. Burgers’s equation is offered for modeling the dynamics of a viscous medium while studying the quantitative properties and classical solutions. An iterative method with new appropriate topological properties is presented to show one classical solution for the problem (1.1) and at least two non-negative classical solutions.</p></div>\",\"PeriodicalId\":55611,\"journal\":{\"name\":\"Aequationes Mathematicae\",\"volume\":\"99 4\",\"pages\":\"1641 - 1655\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-05-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Aequationes Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00010-025-01161-w\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Aequationes Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00010-025-01161-w","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

拟线性微分方程经典解的求解是一个复杂的数学问题，通常需要有限的数学方法才能解决。在研究粘性介质的定量性质和经典解的同时，提出了建立粘性介质动力学模型的Burgers方程。提出了一种具有新的适当拓扑性质的迭代方法，以显示问题（1.1）的一个经典解和至少两个非负经典解。

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

Iterative methods with new topological properties to show a new classical solutions of the Burgers equation

Obtaining the classical solutions of quasi-linear differential equations is a complex mathematical problem usually solved by a limited number of mathematical techniques. Burgers’s equation is offered for modeling the dynamics of a viscous medium while studying the quantitative properties and classical solutions. An iterative method with new appropriate topological properties is presented to show one classical solution for the problem (1.1) and at least two non-negative classical solutions.

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

Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.