TY - JOUR
T1 - Decoupling elastic waves and its applications
AU - Liu, Hongyu
AU - Xiao, Jingni
N1 - Funding Information:
The authors would like to thank the anonymous referee for many constructive comments, which have led to significant improvements on the results and presentation of this paper. The work was supported by the startup fund and the FRG grants from Hong Kong Baptist University, Hong Kong RGC General Research Fund, No. 12302415.
PY - 2017/10/15
Y1 - 2017/10/15
N2 - In this paper, we consider time-harmonic elastic wave scattering governed by the Lamé system. It is known that the elastic wave field can be decomposed into the shear and compressional parts, namely, the pressure and shear waves that are generally coexisting, but propagating at different speeds. We consider the third or fourth kind impenetrable scatterer and derive two geometric conditions, respectively, related to the mean and Gaussian curvatures of the boundary surface of the scatterer that can ensure the decoupling of the shear and pressure waves. The decoupling results are new to the literature and are of significant interest for their own sake. As an interesting application, we apply the decoupling results to the uniqueness and stability analysis for inverse elastic scattering problems in determining polyhedral scatterers by a minimal number of far-field measurements.
AB - In this paper, we consider time-harmonic elastic wave scattering governed by the Lamé system. It is known that the elastic wave field can be decomposed into the shear and compressional parts, namely, the pressure and shear waves that are generally coexisting, but propagating at different speeds. We consider the third or fourth kind impenetrable scatterer and derive two geometric conditions, respectively, related to the mean and Gaussian curvatures of the boundary surface of the scatterer that can ensure the decoupling of the shear and pressure waves. The decoupling results are new to the literature and are of significant interest for their own sake. As an interesting application, we apply the decoupling results to the uniqueness and stability analysis for inverse elastic scattering problems in determining polyhedral scatterers by a minimal number of far-field measurements.
KW - Decoupling
KW - Elastic scattering
KW - Inverse elastic scattering
KW - Lamé system
KW - Shear and pressure waves
KW - Uniqueness and stability
UR - http://www.scopus.com/inward/record.url?scp=85020110051&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2017.05.022
DO - 10.1016/j.jde.2017.05.022
M3 - Journal article
AN - SCOPUS:85020110051
SN - 0022-0396
VL - 263
SP - 4442
EP - 4480
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 8
ER -