Uniqueness and stability of time and space-dependent conductivity in a hyperbolic cylindrical domain

2016/07/05 by Larisa Beilina, Beilina, L., Michel Cristofol +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical Analysis (math.NA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1607.01615

openalex publication_date 2016/07/05 · openalex created_date 2016/07/22 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to the reconstruction of the time and space-dependent coefficient in an infinite cylindrical hyperbolic domain. Using a local Carleman estimate we prove the uniqueness and a Hölder stability in the determining of the conductivity by a single measurement on the lateral boundary. Our numerical examples show good reconstruction of the location and contrast of the conductivity function in three dimensions.

Citations

• On the partial differential equations of mathematical physics

Related

• Determining the waveguide conductivity in a hyperbolic equation from a single measurement on the lateral boundary
• Determining an anisotropic conductivity by boundary measurements: stability at the boundary
• Global uniqueness from partial Cauchy data in two dimensions
• A note on uniqueness in the identification of a spacewise dependent source and diffusion coefficient for the heat equation
• Partial Data for the Calderon Problem in Two Dimensions