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: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/ijmm/2756189 |
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| _version_ | 1849712634816888832 |
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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. |
| format | Article |
| id | doaj-art-6af28a84dfcb443e9aba187a237f644a |
| institution | DOAJ |
| issn | 1687-0425 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |
| work_keys_str_mv | AT umbetkulkoilyshov solutiontoinitialboundaryvalueproblemfortheheatconductivityequationwithadiscontinuouscoefficientandgeneralconjugationconditions AT makhmudsadybekov solutiontoinitialboundaryvalueproblemfortheheatconductivityequationwithadiscontinuouscoefficientandgeneralconjugationconditions AT kulnyarbeisenbayeva solutiontoinitialboundaryvalueproblemfortheheatconductivityequationwithadiscontinuouscoefficientandgeneralconjugationconditions |