Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 262, Issue 1, Pages 653-681Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2016.09.036
Keywords
Inverse source problem; Hyperbolic equation; Carleman estimate; Iterative thresholding algorithm
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Funding
- Grants-in-Aid for Scientific Research [16F16319] Funding Source: KAKEN
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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 Holder 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. (C) 2016 Elsevier Inc. All rights reserved.
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