Inverse Problem for the Schrödinger Equation in Dimension 3
In this paper, we consider the Schrödinger equation in the unit ball in ℝ3. We study the inverse problem of identifying the potential q from the Dirichlet to Neumann map which associates to all possible functions f on the boundary ∂B and the measurements of the normal derivative of the solution of S...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/2935392 |
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| _version_ | 1849468883654672384 |
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| author | Fagueye Ndiaye |
| author_facet | Fagueye Ndiaye |
| author_sort | Fagueye Ndiaye |
| collection | DOAJ |
| description | In this paper, we consider the Schrödinger equation in the unit ball in ℝ3. We study the inverse problem of identifying the potential q from the Dirichlet to Neumann map which associates to all possible functions f on the boundary ∂B and the measurements of the normal derivative of the solution of Schrödinger equation ∂u/∂ν on ∂B. Using spherical harmonics tools, we determine an explicit expression for the potential qx on the edge of the domain from an explicit formula for the Dirichlet to Neumann map in a unit ball in dimension 3. We theoretically and numerically present an example. |
| format | Article |
| id | doaj-art-f3d364bf2d624f2fb8cc0ab3e82ff9a3 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-f3d364bf2d624f2fb8cc0ab3e82ff9a32025-08-20T03:25:42ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/2935392Inverse Problem for the Schrödinger Equation in Dimension 3Fagueye Ndiaye0Departement of MathematicsIn this paper, we consider the Schrödinger equation in the unit ball in ℝ3. We study the inverse problem of identifying the potential q from the Dirichlet to Neumann map which associates to all possible functions f on the boundary ∂B and the measurements of the normal derivative of the solution of Schrödinger equation ∂u/∂ν on ∂B. Using spherical harmonics tools, we determine an explicit expression for the potential qx on the edge of the domain from an explicit formula for the Dirichlet to Neumann map in a unit ball in dimension 3. We theoretically and numerically present an example.http://dx.doi.org/10.1155/2022/2935392 |
| spellingShingle | Fagueye Ndiaye Inverse Problem for the Schrödinger Equation in Dimension 3 Journal of Mathematics |
| title | Inverse Problem for the Schrödinger Equation in Dimension 3 |
| title_full | Inverse Problem for the Schrödinger Equation in Dimension 3 |
| title_fullStr | Inverse Problem for the Schrödinger Equation in Dimension 3 |
| title_full_unstemmed | Inverse Problem for the Schrödinger Equation in Dimension 3 |
| title_short | Inverse Problem for the Schrödinger Equation in Dimension 3 |
| title_sort | inverse problem for the schrodinger equation in dimension 3 |
| url | http://dx.doi.org/10.1155/2022/2935392 |
| work_keys_str_mv | AT fagueyendiaye inverseproblemfortheschrodingerequationindimension3 |