On the integral equation of an adjoint boundary value problem of heat conduction
An integral equation is considered, to which a nonhomogeneous first boundary value problem with an adjoint heat conduction operator is reduced. The problem is set in an infinite plane angle, that is, a boundary of the domain moves with a constant velocity, and the domain degenerates to a point at t...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2019-09-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/271 |
| _version_ | 1797372650744446976 |
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| author | M.T. Kosmakova V.G. Romanovski N.T. Orumbayeva Zh.M. Tuleutaeva L.Zh. Kasymova |
| author_facet | M.T. Kosmakova V.G. Romanovski N.T. Orumbayeva Zh.M. Tuleutaeva L.Zh. Kasymova |
| author_sort | M.T. Kosmakova |
| collection | DOAJ |
| description |
An integral equation is considered, to which a nonhomogeneous first boundary value problem with an adjoint heat conduction operator is reduced. The problem is set in an infinite plane angle, that is, a boundary of the domain moves with a constant velocity, and the domain degenerates to a point at the initial moment of time. The incompressibility of the integral operator for the equation under study is shown. Using the relations for an independent variable, the equation under study is equivalently reduced to a certain simplified equation. With the help of replacements for independent variables, the equation is reduced to an integral equation with a difference kernel. By applying the Laplace transform, the obtained equation is reduced to an ordinary first - order differential equation (linear). Its solution is found. By using the inverse Laplace transform, a solution of the nonhomogeneous integral equation under study is obtained in the form of a convergent series in some domain.
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| first_indexed | 2024-03-08T18:38:54Z |
| format | Article |
| id | doaj.art-5193f8a3ac384e429fde1d80c202fa3e |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:38:54Z |
| publishDate | 2019-09-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-5193f8a3ac384e429fde1d80c202fa3e2023-12-29T10:20:45ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112019-09-0195310.31489/2019m2/33-43On the integral equation of an adjoint boundary value problem of heat conductionM.T. KosmakovaV.G. RomanovskiN.T. OrumbayevaZh.M. TuleutaevaL.Zh. Kasymova An integral equation is considered, to which a nonhomogeneous first boundary value problem with an adjoint heat conduction operator is reduced. The problem is set in an infinite plane angle, that is, a boundary of the domain moves with a constant velocity, and the domain degenerates to a point at the initial moment of time. The incompressibility of the integral operator for the equation under study is shown. Using the relations for an independent variable, the equation under study is equivalently reduced to a certain simplified equation. With the help of replacements for independent variables, the equation is reduced to an integral equation with a difference kernel. By applying the Laplace transform, the obtained equation is reduced to an ordinary first - order differential equation (linear). Its solution is found. By using the inverse Laplace transform, a solution of the nonhomogeneous integral equation under study is obtained in the form of a convergent series in some domain. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/271heat conductionnonhomogeneous singular integral equationadjoint boundary value problemLaplace transform |
| spellingShingle | M.T. Kosmakova V.G. Romanovski N.T. Orumbayeva Zh.M. Tuleutaeva L.Zh. Kasymova On the integral equation of an adjoint boundary value problem of heat conduction Қарағанды университетінің хабаршысы. Математика сериясы heat conduction nonhomogeneous singular integral equation adjoint boundary value problem Laplace transform |
| title | On the integral equation of an adjoint boundary value problem of heat conduction |
| title_full | On the integral equation of an adjoint boundary value problem of heat conduction |
| title_fullStr | On the integral equation of an adjoint boundary value problem of heat conduction |
| title_full_unstemmed | On the integral equation of an adjoint boundary value problem of heat conduction |
| title_short | On the integral equation of an adjoint boundary value problem of heat conduction |
| title_sort | on the integral equation of an adjoint boundary value problem of heat conduction |
| topic | heat conduction nonhomogeneous singular integral equation adjoint boundary value problem Laplace transform |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/271 |
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