Inverse source problem for the space-time fractional parabolic equation on a metric star graph with an integral overdetermination condition
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929479391117312 |
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| author | Ashurov, R. R. Sobirov, Z. A Turemuratova, A. A. |
| author_facet | Ashurov, R. R. Sobirov, Z. A Turemuratova, A. A. |
| contents | In the present paper, we investigate the initial-boundary value problem for fractional order parabolic equation on a metric star graph in Sobolev spaces. First, we prove the existence and uniqueness results of strong solutions which are proved with the classical functional method based on a priori estimates. Moreover, the inverse source problem with the integral overdetermination condition for space-time fractional derivatives in Sobolev spaces is first considered in the present paper. By transforming the inverse problem to the operator-based equation, we showed that the corresponding resolvent operator is well-defined. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_17144 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inverse source problem for the space-time fractional parabolic equation on a metric star graph with an integral overdetermination condition Ashurov, R. R. Sobirov, Z. A Turemuratova, A. A. Analysis of PDEs 35D35, 35R02, 35R11 In the present paper, we investigate the initial-boundary value problem for fractional order parabolic equation on a metric star graph in Sobolev spaces. First, we prove the existence and uniqueness results of strong solutions which are proved with the classical functional method based on a priori estimates. Moreover, the inverse source problem with the integral overdetermination condition for space-time fractional derivatives in Sobolev spaces is first considered in the present paper. By transforming the inverse problem to the operator-based equation, we showed that the corresponding resolvent operator is well-defined. |
| title | Inverse source problem for the space-time fractional parabolic equation on a metric star graph with an integral overdetermination condition |
| topic | Analysis of PDEs 35D35, 35R02, 35R11 |
| url | https://arxiv.org/abs/2408.17144 |