具有幂退化的混合抛物型双曲型方程的逆问题

IF 0.9 4区数学 Q2 MATHEMATICS

Journal of Inverse and Ill-Posed Problems Pub Date : 2023-02-28 DOI:10.1515/jiip-2020-0154

K. Sabitov, S. Sidorov

{"title":"具有幂退化的混合抛物型双曲型方程的逆问题","authors":"K. Sabitov, S. Sidorov","doi":"10.1515/jiip-2020-0154","DOIUrl":null,"url":null,"abstract":"Abstract For the equation of a mixed parabolic-hyperbolic type with a power degeneration on the type change line, the inverse problems to determine the time-dependent factors of right-hand sides are studied. Based on the formula for solving a direct problem, the solution of inverse problems is equivalently reduced to the solvability of loaded integral equations. Using the theory of integral equations, the corresponding theorems for the existence and uniqueness of the solutions of the stated inverse problems are proved and the explicit formulas for the solution have been given.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":" ","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Inverse problems for equations of a mixed parabolic-hyperbolic type with power degeneration in finding the right-hand parts that depend on time\",\"authors\":\"K. Sabitov, S. Sidorov\",\"doi\":\"10.1515/jiip-2020-0154\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract For the equation of a mixed parabolic-hyperbolic type with a power degeneration on the type change line, the inverse problems to determine the time-dependent factors of right-hand sides are studied. Based on the formula for solving a direct problem, the solution of inverse problems is equivalently reduced to the solvability of loaded integral equations. Using the theory of integral equations, the corresponding theorems for the existence and uniqueness of the solutions of the stated inverse problems are proved and the explicit formulas for the solution have been given.\",\"PeriodicalId\":50171,\"journal\":{\"name\":\"Journal of Inverse and Ill-Posed Problems\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Inverse and Ill-Posed Problems\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/jiip-2020-0154\",\"RegionNum\":4,\"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":"Journal of Inverse and Ill-Posed Problems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/jiip-2020-0154","RegionNum":4,"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

摘要针对一类在变型线上有幂退化的混合抛物-双曲型方程，研究了确定方程右侧时因因子的逆问题。基于求解正问题的公式，将反问题的解等效化为加载积分方程的可解性。利用积分方程理论，证明了所述反问题解的存在唯一性定理，并给出了解的显式公式。

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

Inverse problems for equations of a mixed parabolic-hyperbolic type with power degeneration in finding the right-hand parts that depend on time

Abstract For the equation of a mixed parabolic-hyperbolic type with a power degeneration on the type change line, the inverse problems to determine the time-dependent factors of right-hand sides are studied. Based on the formula for solving a direct problem, the solution of inverse problems is equivalently reduced to the solvability of loaded integral equations. Using the theory of integral equations, the corresponding theorems for the existence and uniqueness of the solutions of the stated inverse problems are proved and the explicit formulas for the solution have been given.

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

Journal of Inverse and Ill-Posed Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： This journal aims to present original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published. Issues of the Journal of Inverse and Ill-Posed Problems contain high quality papers which have an innovative approach and topical interest. The following topics are covered: Inverse problems existence and uniqueness theorems stability estimates optimization and identification problems numerical methods Ill-posed problems regularization theory operator equations integral geometry Applications inverse problems in geophysics, electrodynamics and acoustics inverse problems in ecology inverse and ill-posed problems in medicine mathematical problems of tomography