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Choudhury, A.P. and Heck, H. (2017) Increasing Stability for the Inverse Problem for the Schrödinger Equation. Mathematics. Mathematical Methods in the Applied Sciences, 41, 606-614.

has been cited by the following article:

• TITLE: Dirichlet-to-Neumann Map for a Hyperbolic Equation

  AUTHORS: Fagueye Ndiaye, Mouhamadou Ngom, Diaraf Seck

  KEYWORDS: Hyperbolic Differential Equation, Calderón’s Problem, Schrödinger Operator, Potential, Inverse Potential Problem, Dirichlet-to-Neumann Map, Numerical Simulations, Lipschitz Stability

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.8, August 15, 2023

  ABSTRACT: In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann operators corresponding to a potential radial have the same properties for hyperbolic differential equations as for elliptic differential equations. We numerically implement the coefficients of the explicit formulas. Moreover, a Lipschitz type stability is established near the edge of the domain by an estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neumann map in the inverse problem for a hyperbolic differential equation.