INTEGRAL TRANSFORMATION FOR THE THIRD BOUNDARY-VALUE PROBLEM OF NON-STATIONARY HEAT CONDUCTIVITY WITH A CONTINUOUS SPECTRUM OF EIGENVALUES
The mathematical theory of constructing an integral transformation and the inversion formula for it for the third boundary value problem in a domain with a continuous spectrum of eigenvalues are developed. The method is based on the operational solution of the initial problem with an initial functio...
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| Format: | Article |
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MIREA - Russian Technological University
2017-06-01
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| Series: | Тонкие химические технологии |
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| Online Access: | https://www.finechem-mirea.ru/jour/article/view/97 |
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| author | E. M. Kartashov |
| author_facet | E. M. Kartashov |
| author_sort | E. M. Kartashov |
| collection | DOAJ |
| description | The mathematical theory of constructing an integral transformation and the inversion formula for it for the third boundary value problem in a domain with a continuous spectrum of eigenvalues are developed. The method is based on the operational solution of the initial problem with an initial function of general form satisfying the Dirichlet condition and a homogeneous boundary condition of the third kind. On the basis of the obtained relations, a series of analytical solutions of the third boundary value problem for a parabolic equation in various equivalent functional forms is proposed. An integral representation of the analytic solutions of the third boundary-value problem is proposed for the general form of the representation of boundary-value functions in the initial formulation of the problem. The corresponding Green's function is written out. |
| format | Article |
| id | doaj-art-8804b40e683b4cdf869cc16e1a9db037 |
| institution | Kabale University |
| issn | 2410-6593 2686-7575 |
| language | Russian |
| publishDate | 2017-06-01 |
| publisher | MIREA - Russian Technological University |
| record_format | Article |
| series | Тонкие химические технологии |
| spelling | doaj-art-8804b40e683b4cdf869cc16e1a9db0372025-08-20T03:56:33ZrusMIREA - Russian Technological UniversityТонкие химические технологии2410-65932686-75752017-06-01123818610.32362/2410-6593-2017-12-3-81-8697INTEGRAL TRANSFORMATION FOR THE THIRD BOUNDARY-VALUE PROBLEM OF NON-STATIONARY HEAT CONDUCTIVITY WITH A CONTINUOUS SPECTRUM OF EIGENVALUESE. M. Kartashov0Moscow Technological University (Institute of Fine Chemical Technologies)The mathematical theory of constructing an integral transformation and the inversion formula for it for the third boundary value problem in a domain with a continuous spectrum of eigenvalues are developed. The method is based on the operational solution of the initial problem with an initial function of general form satisfying the Dirichlet condition and a homogeneous boundary condition of the third kind. On the basis of the obtained relations, a series of analytical solutions of the third boundary value problem for a parabolic equation in various equivalent functional forms is proposed. An integral representation of the analytic solutions of the third boundary-value problem is proposed for the general form of the representation of boundary-value functions in the initial formulation of the problem. The corresponding Green's function is written out.https://www.finechem-mirea.ru/jour/article/view/97the third boundary value problemsemi-bounded domainintegral transformationformula of treatmentanalytical solutions |
| spellingShingle | E. M. Kartashov INTEGRAL TRANSFORMATION FOR THE THIRD BOUNDARY-VALUE PROBLEM OF NON-STATIONARY HEAT CONDUCTIVITY WITH A CONTINUOUS SPECTRUM OF EIGENVALUES Тонкие химические технологии the third boundary value problem semi-bounded domain integral transformation formula of treatment analytical solutions |
| title | INTEGRAL TRANSFORMATION FOR THE THIRD BOUNDARY-VALUE PROBLEM OF NON-STATIONARY HEAT CONDUCTIVITY WITH A CONTINUOUS SPECTRUM OF EIGENVALUES |
| title_full | INTEGRAL TRANSFORMATION FOR THE THIRD BOUNDARY-VALUE PROBLEM OF NON-STATIONARY HEAT CONDUCTIVITY WITH A CONTINUOUS SPECTRUM OF EIGENVALUES |
| title_fullStr | INTEGRAL TRANSFORMATION FOR THE THIRD BOUNDARY-VALUE PROBLEM OF NON-STATIONARY HEAT CONDUCTIVITY WITH A CONTINUOUS SPECTRUM OF EIGENVALUES |
| title_full_unstemmed | INTEGRAL TRANSFORMATION FOR THE THIRD BOUNDARY-VALUE PROBLEM OF NON-STATIONARY HEAT CONDUCTIVITY WITH A CONTINUOUS SPECTRUM OF EIGENVALUES |
| title_short | INTEGRAL TRANSFORMATION FOR THE THIRD BOUNDARY-VALUE PROBLEM OF NON-STATIONARY HEAT CONDUCTIVITY WITH A CONTINUOUS SPECTRUM OF EIGENVALUES |
| title_sort | integral transformation for the third boundary value problem of non stationary heat conductivity with a continuous spectrum of eigenvalues |
| topic | the third boundary value problem semi-bounded domain integral transformation formula of treatment analytical solutions |
| url | https://www.finechem-mirea.ru/jour/article/view/97 |
| work_keys_str_mv | AT emkartashov integraltransformationforthethirdboundaryvalueproblemofnonstationaryheatconductivitywithacontinuousspectrumofeigenvalues |