An inverse kinematic problem with internal sources

被引：4

作者：

Pestov, Leonid ^{[1
]}

Uhlmann, Gunther ^{[2
,3
]}

Zhou, Hanming ^{[2
]}

机构：

[1] Immanuel Kant Baltic Fed Univ, Kaliningrad, Russia

[2] Univ Washington, Dept Math, Seattle, WA 98195 USA

[3] Hong Kong Univ Sci & Technol, IAS, Hong Kong, Hong Kong, Peoples R China

来源：

INVERSE PROBLEMS | 2015年 / 31卷 / 05期

关键词：

inverse kinematic; internal data; conformal Killing vector fields; RIGIDITY;

D O I：

10.1088/0266-5611/31/5/055006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a bounded domain M in R-n with a conformally Euclidean metric g = rho dx(2), we consider the inverse problem of recovering a semigeodesic neighborhood of a domain Gamma subset of partial derivative M and the conformal factor rho in the neighborhood from the travel time data (defined below) and the Cartesian coordinates of Gamma. 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.

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页数：6

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