TY - JOUR
T1 - Determining a fractional Helmholtz equation with unknown source and scattering potential
AU - Cao, Xinlin
AU - Liu, Hongyu
N1 - Funding Information:
Acknowledgement. The authors would like to thank the two anonymous referees for many constructive comments and suggestions, which have led to significant improvements in the results and presentation of the paper. We would also like to thank Dr. Yi-Hsuan Lin for helpful discussion. H. Liu was supported by the FRG and startup grants from Hong Kong Baptist University, and Hong Kong RGC General Research Funds, 12302017 and 12301218.
PY - 2020/1/6
Y1 - 2020/1/6
N2 - We are concerned with an inverse problem associated with a fractional Helmholtz equation that arises from the study of viscoacoustics in geophysics and thermoviscous modelling of lossy media. We are particularly interested in the case that both the medium parameter and the internal source of the wave equation are unknown. Moreover, we consider a general class of source functions which can be frequency-dependent. We establish several general uniqueness results in simultaneously recovering both the medium parameter and the internal source by the corresponding exterior measurements. In sharp contrast, these unique determination results are unknown in the local case, which would be of significant importance in thermo-and photo-acoustic tomography.
AB - We are concerned with an inverse problem associated with a fractional Helmholtz equation that arises from the study of viscoacoustics in geophysics and thermoviscous modelling of lossy media. We are particularly interested in the case that both the medium parameter and the internal source of the wave equation are unknown. Moreover, we consider a general class of source functions which can be frequency-dependent. We establish several general uniqueness results in simultaneously recovering both the medium parameter and the internal source by the corresponding exterior measurements. In sharp contrast, these unique determination results are unknown in the local case, which would be of significant importance in thermo-and photo-acoustic tomography.
KW - Compact embedding theorem
KW - Fractional helmholtz equation
KW - Low-frequency asymptotics
KW - Runge approximation property
KW - Simultaneous recovery
KW - Strong uniqueness property
UR - http://www.scopus.com/inward/record.url?scp=85078523556&partnerID=8YFLogxK
U2 - 10.4310/CMS.2019.v17.n7.a5
DO - 10.4310/CMS.2019.v17.n7.a5
M3 - Journal article
AN - SCOPUS:85078523556
SN - 1539-6746
VL - 17 (2019)
SP - 1861
EP - 1876
JO - Communications in Mathematical Sciences
JF - Communications in Mathematical Sciences
IS - 7
ER -