确定具有特征类型变化线的抛物线-双曲混合方程中的源函数

IF 0.8 Q2 MATHEMATICS
D. K. Durdiev, D. A. Toshev, H. H. Turdiev
{"title":"确定具有特征类型变化线的抛物线-双曲混合方程中的源函数","authors":"D. K. Durdiev, D. A. Toshev, H. H. Turdiev","doi":"10.1134/s1995080224600584","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we study the direct and inverse problems for a model equation of a mixed parabolic-hyperbolic type. In the direct problem, an analog of the Tricomi problem for this equation with a characteristic line of type change is considered. The unknown of the inverse problem is the y-dependent source function of the parabolic equation. To determine it with respect to the solution defined in the parabolic part of the domain, an overdetermination at the point <span>\\(x=x_{0}\\)</span> for <span>\\(y&gt;0\\)</span> condition is specified. Local theorems on the unique solvability of the problems posed in the sense of the classical solution are proved.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"27 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Determining a Source Function in the Mixed Parabolic–Hyperbolic Equation with Characteristic Type Change Line\",\"authors\":\"D. K. Durdiev, D. A. Toshev, H. H. Turdiev\",\"doi\":\"10.1134/s1995080224600584\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>In this paper, we study the direct and inverse problems for a model equation of a mixed parabolic-hyperbolic type. In the direct problem, an analog of the Tricomi problem for this equation with a characteristic line of type change is considered. The unknown of the inverse problem is the y-dependent source function of the parabolic equation. To determine it with respect to the solution defined in the parabolic part of the domain, an overdetermination at the point <span>\\\\(x=x_{0}\\\\)</span> for <span>\\\\(y&gt;0\\\\)</span> condition is specified. Local theorems on the unique solvability of the problems posed in the sense of the classical solution are proved.</p>\",\"PeriodicalId\":46135,\"journal\":{\"name\":\"Lobachevskii Journal of Mathematics\",\"volume\":\"27 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-07-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Lobachevskii Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1134/s1995080224600584\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995080224600584","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

摘要 本文研究了抛物-双曲混合型模型方程的直接问题和逆问题。在直接问题中,我们考虑了该方程的 Tricomi 问题的类似问题,其特征线类型发生了变化。逆问题的未知数是抛物线方程的 y 依赖源函数。为了确定它与定义在抛物线部分域中的解的关系,在点\(x=x_{0}\)处指定了一个\(y>0\)条件的过度确定。证明了在经典解的意义上所提出问题的唯一可解性的局部定理。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Determining a Source Function in the Mixed Parabolic–Hyperbolic Equation with Characteristic Type Change Line

Abstract

In this paper, we study the direct and inverse problems for a model equation of a mixed parabolic-hyperbolic type. In the direct problem, an analog of the Tricomi problem for this equation with a characteristic line of type change is considered. The unknown of the inverse problem is the y-dependent source function of the parabolic equation. To determine it with respect to the solution defined in the parabolic part of the domain, an overdetermination at the point \(x=x_{0}\) for \(y>0\) condition is specified. Local theorems on the unique solvability of the problems posed in the sense of the classical solution are proved.

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
CiteScore
1.50
自引率
42.90%
发文量
127
期刊介绍: Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信