TY - JOUR
T1 - Inverse source problem for a system of wave equations on a Lorentzian manifold
AU - Takase, Hiroshi
N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Number JP20J11497. The author thanks Professor Masahiro Yamamoto (The University of Tokyo) for many valuable discussions and comments and thanks also the anonymous referees for invaluable comments.
Publisher Copyright:
© 2020 The Author(s). Published with license by Taylor and Francis Group, LLC.
PY - 2020/10/2
Y1 - 2020/10/2
N2 - A system of wave equations on a Lorentzian manifold, the coefficients of which depend on time relates to the Einstein equation in general relativity. We consider inverse source problem for the system in this paper. Having established the Carleman estimate with a second large parameter for the Laplace–Beltrami operator on a Lorentzian manifold under assumptions independent of a choice of local coordinates on a suitable weight function, we consider its application to the inverse source problem for the system and prove local Hölder stability.
AB - A system of wave equations on a Lorentzian manifold, the coefficients of which depend on time relates to the Einstein equation in general relativity. We consider inverse source problem for the system in this paper. Having established the Carleman estimate with a second large parameter for the Laplace–Beltrami operator on a Lorentzian manifold under assumptions independent of a choice of local coordinates on a suitable weight function, we consider its application to the inverse source problem for the system and prove local Hölder stability.
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U2 - 10.1080/03605302.2020.1774897
DO - 10.1080/03605302.2020.1774897
M3 - Article
AN - SCOPUS:85087438320
VL - 45
SP - 1414
EP - 1434
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
SN - 0360-5302
IS - 10
ER -