New type of the unique continuation property for a fractional diffusion equation and an inverse source problem
Abstract In this work, a new type of the unique continuation property for time-fractional diffusion equations is studied. The proof is mainly based on the Laplace transform and the properties of Bessel functions. As an application, the uniqueness of the inverse problem in the simultaneous determinat...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-01-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-024-01827-5 |
| _version_ | 1797276383172362240 |
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| author | Wenyi Liu Chengbin Du Zhiyuan Li |
| author_facet | Wenyi Liu Chengbin Du Zhiyuan Li |
| author_sort | Wenyi Liu |
| collection | DOAJ |
| description | Abstract In this work, a new type of the unique continuation property for time-fractional diffusion equations is studied. The proof is mainly based on the Laplace transform and the properties of Bessel functions. As an application, the uniqueness of the inverse problem in the simultaneous determination of spatially dependent source terms and fractional order from sparse boundary observation data is established. |
| first_indexed | 2024-03-07T15:27:29Z |
| format | Article |
| id | doaj.art-1f0217f9ec76444a88f8eeb4c3c5ff1e |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-03-07T15:27:29Z |
| publishDate | 2024-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-1f0217f9ec76444a88f8eeb4c3c5ff1e2024-03-05T16:36:41ZengSpringerOpenBoundary Value Problems1687-27702024-01-012024111310.1186/s13661-024-01827-5New type of the unique continuation property for a fractional diffusion equation and an inverse source problemWenyi Liu0Chengbin Du1Zhiyuan Li2College of Mechanics and Engineering Science, Hohai UniversityCollege of Mechanics and Engineering Science, Hohai UniversitySchool of Mathematics and Statistics, Ningbo UniversityAbstract In this work, a new type of the unique continuation property for time-fractional diffusion equations is studied. The proof is mainly based on the Laplace transform and the properties of Bessel functions. As an application, the uniqueness of the inverse problem in the simultaneous determination of spatially dependent source terms and fractional order from sparse boundary observation data is established.https://doi.org/10.1186/s13661-024-01827-5Unique continuation propertyFractional diffusion equationInverse source problemUniquenessNeumann boundary data |
| spellingShingle | Wenyi Liu Chengbin Du Zhiyuan Li New type of the unique continuation property for a fractional diffusion equation and an inverse source problem Boundary Value Problems Unique continuation property Fractional diffusion equation Inverse source problem Uniqueness Neumann boundary data |
| title | New type of the unique continuation property for a fractional diffusion equation and an inverse source problem |
| title_full | New type of the unique continuation property for a fractional diffusion equation and an inverse source problem |
| title_fullStr | New type of the unique continuation property for a fractional diffusion equation and an inverse source problem |
| title_full_unstemmed | New type of the unique continuation property for a fractional diffusion equation and an inverse source problem |
| title_short | New type of the unique continuation property for a fractional diffusion equation and an inverse source problem |
| title_sort | new type of the unique continuation property for a fractional diffusion equation and an inverse source problem |
| topic | Unique continuation property Fractional diffusion equation Inverse source problem Uniqueness Neumann boundary data |
| url | https://doi.org/10.1186/s13661-024-01827-5 |
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