Increasing stability in the inverse source problem with many frequencies

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Issue Date
2016-03-05
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Authors
Cheng, Jin
Isakov, Victor
Lu, Shuai
Advisor
Citation

Jin Cheng, Victor Isakov, Shuai Lu, Increasing stability in the inverse source problem with many frequencies, Journal of Differential Equations, Volume 260, Issue 5, 5 March 2016, Pages 4786-4804

Abstract

We study increasing stability in the interior inverse source problem for the Helmholtz equation from boundary Cauchy data for multiple wave numbers. By using the Fourier transform with respect to the wave number, explicit bounds for the analytic continuation, uniqueness of the continuation results, and exact observability bounds for the wave equation, a sharp uniqueness result and an increasing (with larger wave numbers intervals) stability estimate are obtained. Numerical examples in 3 spatial dimension support the theoretical prediction. (C) 2015 Elsevier Inc. All rights reserved.

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