An inverse kinematic problem with internal sources. (24th April 2015)

• Record Type: Journal Article
• Authors: Pestov, Leonid; Uhlmann, Gunther; Zhou, Hanming
• Is Part Of: Inverse problems. Volume 31:Number 5(2015:May)
• Publication Date: 2015-04-24
• Subjects: inverse kinematic -- internal data -- conformal Killing vector fields; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/5/055006
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: Given a bounded domain M in with a conformally Euclidean metric, we consider the inverse problem of recovering a semigeodesic neighborhood of a domain and the conformal factor ρ in the neighborhood from the travel time data (defined below) and the Cartesian coordinates of Γ . We develop an explicit reconstruction procedure for this problem. The key ingredient is the relation between the reconstruction procedure and a Cauchy problem of the conformal Killing equation.