Lipschitz stability for an inverse hyperbolic problem of determining two coefficients by a finite number of observations
Journal article, 2018

We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove Lipschitz stability estimates which ensure unique reconstruction of both coefficients. Our theoretical results are justified by numerical studies on the recon struction of two unknown coefficients using noisy backscattered data.

two space-dependent coefficients

an acoustic equation of hyperbolic type

adaptive algorithm

coefficient inverse problem

Carleman estimate

Author

Larisa Beilina

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

M. Cristofol

Institut de Mathematiques de Marseille

Shumin Li

University of Science and Technology of China

M. Yamamoto

University of Tokyo

RUDN University

Inverse Problems

0266-5611 (ISSN)

Vol. 34 1 015001

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis

DOI

10.1088/1361-6420/aa941d

More information

Latest update

6/24/2019