| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 38 | |
| Number of page(s) | 31 | |
| DOI | https://doi.org/10.1051/cocv/2023031 | |
| Published online | 09 June 2023 | |
Stability of inverse source problem for a transmission wave equation with multiple interfaces of discontinuity*
1
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences,
Beijing 100190,
PR China
2
School of Mathematical Sciences, University of Chinese Academy of Sciences,
Beijing 100049,
PR China
** Corresponding author: zws@lsec.cc.ac.cn
Received:
22
December
2021
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
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