Volume 29, 2023
|Number of page(s)||31|
|Published online||09 June 2023|
Stability of inverse source problem for a transmission wave equation with multiple interfaces of discontinuity*
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences,
2 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
** Corresponding author: email@example.com
Accepted: 19 April 2023
In this paper, we consider a transmission wave equation in N embedded domains with multiple interfaces of discontinuous coefficients in ℝ2. We study the global stability in determining the source term from a one-measurement data of wavefield velocity in a subboundary over a time interval. We prove the stability estimate for this inverse source problem by a combination of the local hyperbolic/elliptic Carleman estimates and the Fourier-Bros-Iagolniter transformation. Our method could be generalized to general dimensions since the weight functions and Carleman estimates are independent of the dimensions.
Mathematics Subject Classification: 35R30 / 35L05 / 35L20
Key words: Carleman estimate / inverse source problem / transmission wave equation / discontinuous coefficient / multiple interfaces
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.