The inverse problem for the heat equation with reflection of the argument and with a complex coefficient
Abstract The paper is devoted to finding a solution and restoring the right-hand side of the heat equation with reflection of the argument in the second derivative, with a complex-valued variable coefficient. We prove a theorem on the Riesz basis property for eigenfunctions of the second-order diffe...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2022-12-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-022-01675-1 |
| _version_ | 1797980471815045120 |
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| author | Elmira Mussirepova Abdissalam Sarsenbi Abdizhahan Sarsenbi |
| author_facet | Elmira Mussirepova Abdissalam Sarsenbi Abdizhahan Sarsenbi |
| author_sort | Elmira Mussirepova |
| collection | DOAJ |
| description | Abstract The paper is devoted to finding a solution and restoring the right-hand side of the heat equation with reflection of the argument in the second derivative, with a complex-valued variable coefficient. We prove a theorem on the Riesz basis property for eigenfunctions of the second-order differential operator with involution in the second derivative. We establish the existence and uniqueness of the solution of the studied problems by the method of separation of variables |
| first_indexed | 2024-04-11T05:56:00Z |
| format | Article |
| id | doaj.art-fc7e9c1cb29e46bfa790251a4578b3c8 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-04-11T05:56:00Z |
| publishDate | 2022-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-fc7e9c1cb29e46bfa790251a4578b3c82022-12-22T04:41:55ZengSpringerOpenBoundary Value Problems1687-27702022-12-012022111310.1186/s13661-022-01675-1The inverse problem for the heat equation with reflection of the argument and with a complex coefficientElmira Mussirepova0Abdissalam Sarsenbi1Abdizhahan Sarsenbi2Scientific Center for Theoretical and Applied Mathematics and Department of Mathematics, M. Auezov South Kazakhstan UniversityScientific Center for Theoretical and Applied Mathematics and Department of Mathematics, M. Auezov South Kazakhstan UniversityScientific Center for Theoretical and Applied Mathematics and Department of Mathematics, M. Auezov South Kazakhstan UniversityAbstract The paper is devoted to finding a solution and restoring the right-hand side of the heat equation with reflection of the argument in the second derivative, with a complex-valued variable coefficient. We prove a theorem on the Riesz basis property for eigenfunctions of the second-order differential operator with involution in the second derivative. We establish the existence and uniqueness of the solution of the studied problems by the method of separation of variableshttps://doi.org/10.1186/s13661-022-01675-1Heat equation with involutionNonlocal heat equationEigenfunctionsBoundary value problemReflection of the argumentRiesz basis |
| spellingShingle | Elmira Mussirepova Abdissalam Sarsenbi Abdizhahan Sarsenbi The inverse problem for the heat equation with reflection of the argument and with a complex coefficient Boundary Value Problems Heat equation with involution Nonlocal heat equation Eigenfunctions Boundary value problem Reflection of the argument Riesz basis |
| title | The inverse problem for the heat equation with reflection of the argument and with a complex coefficient |
| title_full | The inverse problem for the heat equation with reflection of the argument and with a complex coefficient |
| title_fullStr | The inverse problem for the heat equation with reflection of the argument and with a complex coefficient |
| title_full_unstemmed | The inverse problem for the heat equation with reflection of the argument and with a complex coefficient |
| title_short | The inverse problem for the heat equation with reflection of the argument and with a complex coefficient |
| title_sort | inverse problem for the heat equation with reflection of the argument and with a complex coefficient |
| topic | Heat equation with involution Nonlocal heat equation Eigenfunctions Boundary value problem Reflection of the argument Riesz basis |
| url | https://doi.org/10.1186/s13661-022-01675-1 |
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