Existence and uniqueness of the solution of a mixed problem for a parabolic equation under nonconventional boundary conditions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929603806756864 |
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| author | Mammadov, Yu. A. Ahmadov, H. I. |
| author_facet | Mammadov, Yu. A. Ahmadov, H. I. |
| contents | In this study, we investigate a mixed problem linked to a second-order parabolic equation, characterized by temporal dependencies and variable~coefficients, and constrained by non-local, non-self-adjoint boundary conditions. By defining precise conditions on the input data, we establish the unique solvability of the problem through a synthesis of the residue and contour integral methods. Moreover, our research yields an explicit analytical solution, facilitating the direct resolution of the stated problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16109 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and uniqueness of the solution of a mixed problem for a parabolic equation under nonconventional boundary conditions Mammadov, Yu. A. Ahmadov, H. I. Analysis of PDEs Mathematical Physics In this study, we investigate a mixed problem linked to a second-order parabolic equation, characterized by temporal dependencies and variable~coefficients, and constrained by non-local, non-self-adjoint boundary conditions. By defining precise conditions on the input data, we establish the unique solvability of the problem through a synthesis of the residue and contour integral methods. Moreover, our research yields an explicit analytical solution, facilitating the direct resolution of the stated problem. |
| title | Existence and uniqueness of the solution of a mixed problem for a parabolic equation under nonconventional boundary conditions |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2411.16109 |