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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Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2022, Vol.2022 (1)
Main Author: Ndiaye, Fagueye
Format: Article
Language:English
Subjects:
Dirichlet problem
Eigenvalues
Electrodes
Inverse problems
Mathematics
Partial differential equations
Schrodinger equation
Spherical harmonics
Tomography
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Summary: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.
ISSN:2314-4629
2314-4785
DOI:10.1155/2022/2935392