A priori and a posteriori estimates for solving one evolutionary inverse problem
This article considers an initial-boundary value problem for a system of parabolic equations, which arises when studying the flow of a binary mixture in a horizontal channel with walls heated non-uniformly. The problem was reduced to a sequence of initial-boundary value problems with Dirichlet or Ne...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2024-04-01
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| Series: | Учёные записки Казанского университета. Серия Физико-математические науки |
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| Online Access: | https://uzakufismat.elpub.ru/jour/article/view/35 |
| _version_ | 1797205419997790208 |
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| author | V. K. Andreev I. V. Stepanova |
| author_facet | V. K. Andreev I. V. Stepanova |
| author_sort | V. K. Andreev |
| collection | DOAJ |
| description | This article considers an initial-boundary value problem for a system of parabolic equations, which arises when studying the flow of a binary mixture in a horizontal channel with walls heated non-uniformly. The problem was reduced to a sequence of initial-boundary value problems with Dirichlet or Neumann conditions. Among them, an inverse problem with a non-local overdetermination condition was distinguished. The solution was constructed using the Fourier method and validated as classical. The behavior of the non-stationary solution at large times was discussed. It was shown that certain functions within the solution tend to their stationary analogs exponentially at large times. For some functions, only boundedness was proved. The problem and its solution are relevant for modeling the thermal modes associated with the separation of liquid mixtures. |
| first_indexed | 2024-04-24T08:50:50Z |
| format | Article |
| id | doaj.art-43efb37e934b43d6a50b2613422364f2 |
| institution | Directory Open Access Journal |
| issn | 2541-7746 2500-2198 |
| language | English |
| last_indexed | 2024-04-24T08:50:50Z |
| publishDate | 2024-04-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета. Серия Физико-математические науки |
| spelling | doaj.art-43efb37e934b43d6a50b2613422364f22024-04-16T11:42:17ZengKazan Federal UniversityУчёные записки Казанского университета. Серия Физико-математические науки2541-77462500-21982024-04-01166152110.26907/2541-7746.2024.1.5-2130A priori and a posteriori estimates for solving one evolutionary inverse problemV. K. Andreev0I. V. Stepanova1Institute of Computational Modelling, Siberian Branch, Russian Academy of SciencesInstitute of Computational Modelling, Siberian Branch, Russian Academy of SciencesThis article considers an initial-boundary value problem for a system of parabolic equations, which arises when studying the flow of a binary mixture in a horizontal channel with walls heated non-uniformly. The problem was reduced to a sequence of initial-boundary value problems with Dirichlet or Neumann conditions. Among them, an inverse problem with a non-local overdetermination condition was distinguished. The solution was constructed using the Fourier method and validated as classical. The behavior of the non-stationary solution at large times was discussed. It was shown that certain functions within the solution tend to their stationary analogs exponentially at large times. For some functions, only boundedness was proved. The problem and its solution are relevant for modeling the thermal modes associated with the separation of liquid mixtures.https://uzakufismat.elpub.ru/jour/article/view/35equation of convective heat and mass transfernon-classical boundary value problemnon-stationary solutiona priori estimateboundedness |
| spellingShingle | V. K. Andreev I. V. Stepanova A priori and a posteriori estimates for solving one evolutionary inverse problem Учёные записки Казанского университета. Серия Физико-математические науки equation of convective heat and mass transfer non-classical boundary value problem non-stationary solution a priori estimate boundedness |
| title | A priori and a posteriori estimates for solving one evolutionary inverse problem |
| title_full | A priori and a posteriori estimates for solving one evolutionary inverse problem |
| title_fullStr | A priori and a posteriori estimates for solving one evolutionary inverse problem |
| title_full_unstemmed | A priori and a posteriori estimates for solving one evolutionary inverse problem |
| title_short | A priori and a posteriori estimates for solving one evolutionary inverse problem |
| title_sort | priori and a posteriori estimates for solving one evolutionary inverse problem |
| topic | equation of convective heat and mass transfer non-classical boundary value problem non-stationary solution a priori estimate boundedness |
| url | https://uzakufismat.elpub.ru/jour/article/view/35 |
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