Inverse source problem for the hyperbolic equation with a time-dependent principal part

In this paper, we investigate the inverse problem on determining the spatial component of the source term in the hyperbolic equation with a time-dependent principal part. Based on a Carleman estimate for general hyperbolic operators, we prove a local stability result of Hölder type in both cases of...

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Bibliographic Details
Published in:Journal of Differential Equations Vol. 262; no. 1; pp. 653 - 681
Main Authors: Jiang, Daijun, Liu, Yikan, Yamamoto, Masahiro
Format: Journal Article
Language:English
Published: Elsevier Inc 05.01.2017
Subjects:
Carleman estimate
Hyperbolic equation
Inverse source problem
Iterative thresholding algorithm
Carleman estimate
65F10
Inverse source problem
35R30
65F22
Hyperbolic equation
Iterative thresholding algorithm
35L20
65M32
ISSN:0022-0396, 1090-2732
Online Access:Get full text
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Summary:In this paper, we investigate the inverse problem on determining the spatial component of the source term in the hyperbolic equation with a time-dependent principal part. Based on a Carleman estimate for general hyperbolic operators, we prove a local stability result of Hölder type in both cases of partial boundary and interior observation data. Numerically, we adopt the classical Tikhonov regularization to reformulate the inverse problem into a related optimization problem, for which we develop an iterative thresholding algorithm by using the corresponding adjoint system. Numerical examples up to three spatial dimensions are presented to demonstrate the accuracy and efficiency of the proposed algorithm.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2016.09.036