Inverse inhomogeneous penetrable obstacle scattering problems in a stratified medium

Guoping Zhan, Lihan Liu
2017 Boundary Value Problems  
In this paper we study the inverse inhomogeneous penetrable obstacle scattering problems in a stratified medium. On the basis of the uniqueness and existence of solutions for the direct scattering by an inhomogeneous penetrable obstacle in a stratified medium, we first establish an a priori estimate of the solution on some part of the penetrable interfaces S i (i = 1, 2), which plays an important role in the inverse scattering problems, and then we prove that both the penetrable interfaces S i
more » ... ble interfaces S i (i = 1, 2) and the refractive index n(x) of the inhomogeneous penetrable obstacle 2 can be uniquely determined from knowledge of the far-field pattern u ∞ ( x, d) ( x, d ∈ S, S is the unit sphere of R 3 ) for an incident plane wave u i (x) = e ik 1 x·d (x ∈ R 3 ).
doi:10.1186/s13661-017-0747-3 fatcat:huaapbkcjbadnbintokdfautpy