Determining the conductivity for a nonautonomous hyperbolic operator in a cylindrical domain

descriptionPublicationkeyboard_double_arrow_right Article 15 Jan 2018 France English Publisher:WileyJournal:Mathematical Methods in the Applied Sciences, volume 41, pages 2,012-2,030 (issn: 0170-4214, eissn: 1099-1476,

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Authors: Larisa Beilina; Michel Cristofol; Shumin Li;

doi: 10.1002/mma.4728

Determining the conductivity for a nonautonomous hyperbolic operator in a cylindrical domain

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Abstract

This paper is devoted to the reconstruction of the conductivity coefficient for a nonautonomous hyperbolic operator an infinite cylindrical domain. Applying a local Carleman estimate, we prove the uniqueness and a Hölder stability in the determination of the conductivity using a single measurement data on the lateral boundary. Our numerical examples show good reconstruction of the location and contrast of the conductivity function in 3 dimensions.

Country

France

Related Organizations

Chinese Academy of Sciences
China (People's Republic of)
Chalmers University of Technology
Sweden
University of Science and Technology of China
China (People's Republic of)
UNIVERSITE D'AIX MARSEILLE
France
University of Gothenburg
Sweden

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Keywords

Inverse problems for PDEs, hyperbolic equation, infinite domain, time- and space-dependent coefficient, Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs, Topological dynamics of nonautonomous systems, Carleman estimate, hyperbolic equations, [INFO.INFO-NA] Computer Science [cs]/Numerical Analysis [cs.NA], inverse problem, time and space-dependent coefficient, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Initial-boundary value problems for second-order hyperbolic equations, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

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