Solution to Initial-Boundary Value Problem for the Heat Conductivity Equation With a Discontinuous Coefficient and General Conjugation Conditions

A solution to the initial-boundary value problem for the heat equation with a discontinuous coefficient and a general conjugation condition is verified using the Fourier method. The problem considered in the paper models the process of heat propagation of a temperature field in a thin rod of finite...

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Main Authors: Umbetkul Кoilyshov, Makhmud Sadybekov, Кulnyar Beisenbayeva
Format: Article
Language:English
Published: Wiley 2025-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/ijmm/2756189
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author Umbetkul Кoilyshov
Makhmud Sadybekov
Кulnyar Beisenbayeva
author_facet Umbetkul Кoilyshov
Makhmud Sadybekov
Кulnyar Beisenbayeva
author_sort Umbetkul Кoilyshov
collection DOAJ
description A solution to the initial-boundary value problem for the heat equation with a discontinuous coefficient and a general conjugation condition is verified using the Fourier method. The problem considered in the paper models the process of heat propagation of a temperature field in a thin rod of finite length, consisting of two sections with different thermal-physical characteristics. In this case, not only the boundary conditions of the first kind are taken into account, but also general conditions at the point of contact of the two media. The existence and uniqueness of a classical solution to the studied problem are proved.
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institution DOAJ
issn 1687-0425
language English
publishDate 2025-01-01
publisher Wiley
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-6af28a84dfcb443e9aba187a237f644a2025-08-20T03:14:12ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252025-01-01202510.1155/ijmm/2756189Solution to Initial-Boundary Value Problem for the Heat Conductivity Equation With a Discontinuous Coefficient and General Conjugation ConditionsUmbetkul Кoilyshov0Makhmud Sadybekov1Кulnyar Beisenbayeva2Department of Differential EquationsDepartment of Differential EquationsDepartment of General EngineeringA solution to the initial-boundary value problem for the heat equation with a discontinuous coefficient and a general conjugation condition is verified using the Fourier method. The problem considered in the paper models the process of heat propagation of a temperature field in a thin rod of finite length, consisting of two sections with different thermal-physical characteristics. In this case, not only the boundary conditions of the first kind are taken into account, but also general conditions at the point of contact of the two media. The existence and uniqueness of a classical solution to the studied problem are proved.http://dx.doi.org/10.1155/ijmm/2756189
spellingShingle Umbetkul Кoilyshov
Makhmud Sadybekov
Кulnyar Beisenbayeva
Solution to Initial-Boundary Value Problem for the Heat Conductivity Equation With a Discontinuous Coefficient and General Conjugation Conditions
International Journal of Mathematics and Mathematical Sciences
title Solution to Initial-Boundary Value Problem for the Heat Conductivity Equation With a Discontinuous Coefficient and General Conjugation Conditions
title_full Solution to Initial-Boundary Value Problem for the Heat Conductivity Equation With a Discontinuous Coefficient and General Conjugation Conditions
title_fullStr Solution to Initial-Boundary Value Problem for the Heat Conductivity Equation With a Discontinuous Coefficient and General Conjugation Conditions
title_full_unstemmed Solution to Initial-Boundary Value Problem for the Heat Conductivity Equation With a Discontinuous Coefficient and General Conjugation Conditions
title_short Solution to Initial-Boundary Value Problem for the Heat Conductivity Equation With a Discontinuous Coefficient and General Conjugation Conditions
title_sort solution to initial boundary value problem for the heat conductivity equation with a discontinuous coefficient and general conjugation conditions
url http://dx.doi.org/10.1155/ijmm/2756189
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AT makhmudsadybekov solutiontoinitialboundaryvalueproblemfortheheatconductivityequationwithadiscontinuouscoefficientandgeneralconjugationconditions
AT kulnyarbeisenbayeva solutiontoinitialboundaryvalueproblemfortheheatconductivityequationwithadiscontinuouscoefficientandgeneralconjugationconditions