Inverse problems for a generalized subdiffusion equation with final overdetermination
We consider two inverse problems for a generalized subdiffusion equation that use the final overdetermination condition. Firstly, we study a problem of reconstruction of a specific space-dependent component in a source term. We prove existence, uniqueness and stability of the solution to this proble...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2019-03-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/6726 |
| _version_ | 1831657518034583552 |
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| author | Nataliia Kinash Jaan Janno |
| author_facet | Nataliia Kinash Jaan Janno |
| author_sort | Nataliia Kinash |
| collection | DOAJ |
| description | We consider two inverse problems for a generalized subdiffusion equation that use the final overdetermination condition. Firstly, we study a problem of reconstruction of a specific space-dependent component in a source term. We prove existence, uniqueness and stability of the solution to this problem. Based on these results, we consider an inverse problem of identification of a space-dependent coefficient of a linear reaction term. We prove the uniqueness and local existence and stability of the solution to this problem. |
| first_indexed | 2024-12-19T17:28:22Z |
| format | Article |
| id | doaj.art-e43cfc32b79246bba74aa9d340372bcf |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-19T17:28:22Z |
| publishDate | 2019-03-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-e43cfc32b79246bba74aa9d340372bcf2022-12-21T20:12:30ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102019-03-0124210.3846/mma.2019.016Inverse problems for a generalized subdiffusion equation with final overdeterminationNataliia Kinash0Jaan Janno1Department of Cybernetics, Tallinn University of Technology Ehitajate tee 5,19086 Tallinn, EstoniaDepartment of Cybernetics, Tallinn University of Technology Ehitajate tee 5,19086 Tallinn, EstoniaWe consider two inverse problems for a generalized subdiffusion equation that use the final overdetermination condition. Firstly, we study a problem of reconstruction of a specific space-dependent component in a source term. We prove existence, uniqueness and stability of the solution to this problem. Based on these results, we consider an inverse problem of identification of a space-dependent coefficient of a linear reaction term. We prove the uniqueness and local existence and stability of the solution to this problem.https://journals.vgtu.lt/index.php/MMA/article/view/6726inverse problemsubdiffusionfinal overdeterminationfractional diffusion |
| spellingShingle | Nataliia Kinash Jaan Janno Inverse problems for a generalized subdiffusion equation with final overdetermination Mathematical Modelling and Analysis inverse problem subdiffusion final overdetermination fractional diffusion |
| title | Inverse problems for a generalized subdiffusion equation with final overdetermination |
| title_full | Inverse problems for a generalized subdiffusion equation with final overdetermination |
| title_fullStr | Inverse problems for a generalized subdiffusion equation with final overdetermination |
| title_full_unstemmed | Inverse problems for a generalized subdiffusion equation with final overdetermination |
| title_short | Inverse problems for a generalized subdiffusion equation with final overdetermination |
| title_sort | inverse problems for a generalized subdiffusion equation with final overdetermination |
| topic | inverse problem subdiffusion final overdetermination fractional diffusion |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/6726 |
| work_keys_str_mv | AT nataliiakinash inverseproblemsforageneralizedsubdiffusionequationwithfinaloverdetermination AT jaanjanno inverseproblemsforageneralizedsubdiffusionequationwithfinaloverdetermination |