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.