Volume 29, 2023
|Number of page(s)
|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: firstname.lastname@example.org
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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