On an Inverse Problem of Reconstructing a Heat Conduction Process from Nonlocal Data
We consider an inverse problem for a one-dimensional heat equation with involution and with periodic boundary conditions with respect to a space variable. This problem simulates the process of heat propagation in a thin closed wire wrapped around a weakly permeable insulation. The inverse problem co...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/8301656 |
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| _version_ | 1832555164227076096 |
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| author | Makhmud A. Sadybekov Gulnar Dildabek Marina B. Ivanova |
| author_facet | Makhmud A. Sadybekov Gulnar Dildabek Marina B. Ivanova |
| author_sort | Makhmud A. Sadybekov |
| collection | DOAJ |
| description | We consider an inverse problem for a one-dimensional heat equation with involution and with periodic boundary conditions with respect to a space variable. This problem simulates the process of heat propagation in a thin closed wire wrapped around a weakly permeable insulation. The inverse problem consists in the restoration (simultaneously with the solution) of an unknown right-hand side of the equation, which depends only on the spatial variable. The conditions for redefinition are initial and final states. Existence and uniqueness results for the given problem are obtained via the method of separation of variables. |
| format | Article |
| id | doaj-art-0ba04e9c3f00402f976bb659c45d80ca |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-0ba04e9c3f00402f976bb659c45d80ca2025-02-03T05:49:21ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/83016568301656On an Inverse Problem of Reconstructing a Heat Conduction Process from Nonlocal DataMakhmud A. Sadybekov0Gulnar Dildabek1Marina B. Ivanova2Institute of Mathematics and Mathematical Modeling, 125 Pushkin Str., 050010 Almaty, KazakhstanInstitute of Mathematics and Mathematical Modeling, 125 Pushkin Str., 050010 Almaty, KazakhstanInstitute of Mathematics and Mathematical Modeling, 125 Pushkin Str., 050010 Almaty, KazakhstanWe consider an inverse problem for a one-dimensional heat equation with involution and with periodic boundary conditions with respect to a space variable. This problem simulates the process of heat propagation in a thin closed wire wrapped around a weakly permeable insulation. The inverse problem consists in the restoration (simultaneously with the solution) of an unknown right-hand side of the equation, which depends only on the spatial variable. The conditions for redefinition are initial and final states. Existence and uniqueness results for the given problem are obtained via the method of separation of variables.http://dx.doi.org/10.1155/2018/8301656 |
| spellingShingle | Makhmud A. Sadybekov Gulnar Dildabek Marina B. Ivanova On an Inverse Problem of Reconstructing a Heat Conduction Process from Nonlocal Data Advances in Mathematical Physics |
| title | On an Inverse Problem of Reconstructing a Heat Conduction Process from Nonlocal Data |
| title_full | On an Inverse Problem of Reconstructing a Heat Conduction Process from Nonlocal Data |
| title_fullStr | On an Inverse Problem of Reconstructing a Heat Conduction Process from Nonlocal Data |
| title_full_unstemmed | On an Inverse Problem of Reconstructing a Heat Conduction Process from Nonlocal Data |
| title_short | On an Inverse Problem of Reconstructing a Heat Conduction Process from Nonlocal Data |
| title_sort | on an inverse problem of reconstructing a heat conduction process from nonlocal data |
| url | http://dx.doi.org/10.1155/2018/8301656 |
| work_keys_str_mv | AT makhmudasadybekov onaninverseproblemofreconstructingaheatconductionprocessfromnonlocaldata AT gulnardildabek onaninverseproblemofreconstructingaheatconductionprocessfromnonlocaldata AT marinabivanova onaninverseproblemofreconstructingaheatconductionprocessfromnonlocaldata |