2018•Mathematical Methods in the Applied SciencesOpen access

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

Larisa Beilina, Michel Cristofol, Shumin Li

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.

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Key concepts: Mathematics, Uniqueness, Operator (biology), Mathematical analysis, Domain (mathematical analysis), Conductivity, Boundary (topology), Stability (learning theory)