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) 13616420 (eISSN)
Vol. 34 1 015001Subject Categories
Computational Mathematics
Probability Theory and Statistics
Mathematical Analysis
DOI
10.1088/1361-6420/aa941d