{"title":"Inverse Problems for Heat Convection System for Incompressible Viscoelastic Fluids","authors":"S. N. Antontsev, Kh. Khompysh","doi":"10.1134/s1995080224601152","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper deals the study some inverse source problems for heat convection system which consists of Kelvin–Voigt equations governing an incompressible viscoelastic non-Newtonian flows and a heat equation. The studying inverse problems consist of recovering a time depended intensity <span>\\(f(t)\\)</span> of a density of external forces and an intensity <span>\\(j(t)\\)</span> of a heat source, in addition to a velocity <span>\\(\\mathbf{v}\\)</span>, a pressure <span>\\(\\pi\\)</span>, and a temperature <span>\\(\\theta\\)</span>. As an additional information two types of integral overdetermination conditions over the domain are considered. For nonlinear inverse problem, under suitable conditions on the data, the local in time existence and uniqueness of weak and strong solutions are established. Some special cases of original inverse problem also investigated which allow global unique solvability.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"25 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-08-22","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/s1995080224601152","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
Abstract
The paper deals the study some inverse source problems for heat convection system which consists of Kelvin–Voigt equations governing an incompressible viscoelastic non-Newtonian flows and a heat equation. The studying inverse problems consist of recovering a time depended intensity \(f(t)\) of a density of external forces and an intensity \(j(t)\) of a heat source, in addition to a velocity \(\mathbf{v}\), a pressure \(\pi\), and a temperature \(\theta\). As an additional information two types of integral overdetermination conditions over the domain are considered. For nonlinear inverse problem, under suitable conditions on the data, the local in time existence and uniqueness of weak and strong solutions are established. Some special cases of original inverse problem also investigated which allow global unique solvability.
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.
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