On the uniqueness of inverse problems for the reduced wave equation with unknown embedded obstacles

Abstract

Abstract In this paper, we consider inverse problems associated with the reduced wave equation on a bounded domain Ω ⊂ R N ( N ⩾ 2 ) for the case where unknown obstacles are embedded in the domain Ω. We show that, if both the leading and 0-order coefficients in the equation are a priori known to be piecewise constant functions, then both the coefficients and embedded obstacles can be simultaneously recovered in terms of the local Dirichlet-to-Neumann map defined on an arbitrary small open subset of the boundary ∂Ω. The method depends on a well-defined coupled PDE-system constructed for the reduced wave equations in a sufficiently small domain and the singularity analysis of solutions near the interface for the model.