Determining the conductivity for a nonautonomous hyperbolic operator in a cylindrical domain. (15th January 2018)

• Record Type: Journal Article
• Authors: Beilina, Larisa; Cristofol, Michel; Li, Shumin
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 5(2018)
• Page Start: 2012
• Page End: 2030
• Publication Date: 2018-01-15
• Subjects: Carleman estimate -- hyperbolic equation -- inverse problem -- infinite domain -- time‐ and space‐dependent coefficient; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4728
• Languages: English
• ISSNs: 0170-4214

Abstract

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.