Stability of inverse source problem for a transmission wave equation with multiple interfaces of discontinuity

Abstract

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.