论一维高兹提克问题的解决方案

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-04-22 DOI:10.1134/s0001434624010024

O. V. Baskov, D. K. Potapov

{"title":"论一维高兹提克问题的解决方案","authors":"O. V. Baskov, D. K. Potapov","doi":"10.1134/s0001434624010024","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A one-dimensional analog of the Goldshtik mathematical model for separated flows in an incompressible fluid is considered. The model is a boundary value problem for a second-order ordinary differential equation with discontinuous right-hand side. Some properties of the solutions of the problem, as well as the properties of the energy functional for different values of vorticity, are established. An approximate solution of the boundary value problem under study is found using the shooting method. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Solutions of the One-Dimensional Goldshtik Problem\",\"authors\":\"O. V. Baskov, D. K. Potapov\",\"doi\":\"10.1134/s0001434624010024\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> A one-dimensional analog of the Goldshtik mathematical model for separated flows in an incompressible fluid is considered. The model is a boundary value problem for a second-order ordinary differential equation with discontinuous right-hand side. Some properties of the solutions of the problem, as well as the properties of the energy functional for different values of vorticity, are established. An approximate solution of the boundary value problem under study is found using the shooting method. </p>\",\"PeriodicalId\":18294,\"journal\":{\"name\":\"Mathematical Notes\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-04-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Notes\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0001434624010024\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Notes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0001434624010024","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要研究了不可压缩流体中分离流动的 Goldshtik 数学模型的一维类似模型。该模型是一个右边不连续的二阶常微分方程的边界值问题。建立了问题解的一些特性以及不同涡度值下能量函数的特性。使用射击法找到了所研究边界值问题的近似解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On Solutions of the One-Dimensional Goldshtik Problem

查看原文本刊更多论文

On Solutions of the One-Dimensional Goldshtik Problem

Abstract

A one-dimensional analog of the Goldshtik mathematical model for separated flows in an incompressible fluid is considered. The model is a boundary value problem for a second-order ordinary differential equation with discontinuous right-hand side. Some properties of the solutions of the problem, as well as the properties of the energy functional for different values of vorticity, are established. An approximate solution of the boundary value problem under study is found using the shooting method.

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

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.