An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions
An initial-boundary-value problem is considered for the one-dimensional diffusion equation with a general convolutional derivative in time and nonclassical boundary conditions. We are concerned with the inverse source problem of recovery of a space-dependent source term from given final time data. G...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/5/3/63 |
| _version_ | 1797528167759478784 |
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| author | Emilia Bazhlekova |
| author_facet | Emilia Bazhlekova |
| author_sort | Emilia Bazhlekova |
| collection | DOAJ |
| description | An initial-boundary-value problem is considered for the one-dimensional diffusion equation with a general convolutional derivative in time and nonclassical boundary conditions. We are concerned with the inverse source problem of recovery of a space-dependent source term from given final time data. Generalized eigenfunction expansions are used with respect to a biorthogonal pair of bases. Existence, uniqueness and stability estimates in Sobolev spaces are established. |
| first_indexed | 2024-03-10T09:54:19Z |
| format | Article |
| id | doaj.art-f57454681d9b4578b08c0156945750f1 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T09:54:19Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-f57454681d9b4578b08c0156945750f12023-11-22T02:30:22ZengMDPI AGFractal and Fractional2504-31102021-06-01536310.3390/fractalfract5030063An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary ConditionsEmilia Bazhlekova0Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, BulgariaAn initial-boundary-value problem is considered for the one-dimensional diffusion equation with a general convolutional derivative in time and nonclassical boundary conditions. We are concerned with the inverse source problem of recovery of a space-dependent source term from given final time data. Generalized eigenfunction expansions are used with respect to a biorthogonal pair of bases. Existence, uniqueness and stability estimates in Sobolev spaces are established.https://www.mdpi.com/2504-3110/5/3/63subdiffusion equationinverse source problemRiesz basisMittag–Leffler functionStieltjes function |
| spellingShingle | Emilia Bazhlekova An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions Fractal and Fractional subdiffusion equation inverse source problem Riesz basis Mittag–Leffler function Stieltjes function |
| title | An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions |
| title_full | An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions |
| title_fullStr | An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions |
| title_full_unstemmed | An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions |
| title_short | An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions |
| title_sort | inverse source problem for the generalized subdiffusion equation with nonclassical boundary conditions |
| topic | subdiffusion equation inverse source problem Riesz basis Mittag–Leffler function Stieltjes function |
| url | https://www.mdpi.com/2504-3110/5/3/63 |
| work_keys_str_mv | AT emiliabazhlekova aninversesourceproblemforthegeneralizedsubdiffusionequationwithnonclassicalboundaryconditions AT emiliabazhlekova inversesourceproblemforthegeneralizedsubdiffusionequationwithnonclassicalboundaryconditions |