Linearized boundary control method for an acoustic inverse boundary value problem. (1st November 2022)

• Record Type: Journal Article
• Authors: Oksanen, Lauri; Yang, Tianyu; Yang, Yang
• Is Part Of: Inverse problems. Volume 38:Number 11(2022)
• Publication Date: 2022-11-01
• Subjects: acoustic wave equation -- inverse boundary value problem -- Neumann-to-Dirichlet map -- boundary control method; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac91eb
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We develop a linearized boundary control method for the inverse boundary value problem of determining a potential in the acoustic wave equation from the Neumann-to-Dirichlet map. When the linearization is at the zero potential, we derive a reconstruction formula based on the boundary control method and prove that it is of Lipschitz-type stability. When the linearization is at a nonzero potential, we prove that the problem is of Hölder-type stability in two and higher dimensions. The proposed reconstruction formula is implemented and evaluated using several numerical experiments to validate its feasibility.