Dirichlet-to-Neumann Map for a Hyperbolic Equation

作     者：Fagueye Ndiaye Mouhamadou Ngom Diaraf Seck Fagueye Ndiaye;Mouhamadou Ngom;Diaraf Seck

作者机构：Department of Mathematics Cheikh Anta Diop University Dakar-Fann Senegal Alioune Diop University Bambey Senegal Cheikh Anta Diop University of Dakar Dakar Fann Senegal 

出 版 物：《Journal of Applied Mathematics and Physics》 (应用数学与应用物理（英文）)

年 卷 期：2023年第11卷第8期

页      面：2231-2251页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

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

摘      要：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.