On an Inverse Problem of Reconstructing a Heat Conduction Process from Nonlocal Data

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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Main Authors: Makhmud A. Sadybekov, Gulnar Dildabek, Marina B. Ivanova
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2018/8301656
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spelling doaj-0ba04e9c3f00402f976bb659c45d80ca2021-07-02T06:50:02ZengHindawi LimitedAdvances 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
collection DOAJ
language English
format Article
sources DOAJ
author Makhmud A. Sadybekov
Gulnar Dildabek
Marina B. Ivanova
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
author_facet Makhmud A. Sadybekov
Gulnar Dildabek
Marina B. Ivanova
author_sort Makhmud A. Sadybekov
title 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_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_sort on an inverse problem of reconstructing a heat conduction process from nonlocal data
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2018-01-01
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.
url http://dx.doi.org/10.1155/2018/8301656
work_keys_str_mv AT makhmudasadybekov onaninverseproblemofreconstructingaheatconductionprocessfromnonlocaldata
AT gulnardildabek onaninverseproblemofreconstructingaheatconductionprocessfromnonlocaldata
AT marinabivanova onaninverseproblemofreconstructingaheatconductionprocessfromnonlocaldata
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