期刊
INVERSE PROBLEMS
卷 34, 期 4, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1361-6420/aaa4a0
关键词
hyperbolic equation; coefficient inverse problem; Carleman estimate; local Holder stability; iteration method
资金
- A3 Foresight Program 'Modeling and Computation of Applied Inverse Problems', Japan Society for the Promotion of Science (JSPS)
- National Natural Science Foundation of China
- NSFC [11331004, 11421110002]
- Programme of Introducing Talents of Discipline to Universities [B08018]
- JSPS KAKENHI [JP15H05740, JP16F16319]
- JSPS Postdoctoral Fellowship for Overseas Researchers
- Ministry of Education and Science of the Russian Federation [02a03.21.0008]
In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numerical aspects. By the Carleman estimates for general hyperbolic operators and an auxiliary Carleman estimate, we establish local Holder stability with either partial boundary or interior measurements under certain geometrical conditions. For numerical reconstruction, we minimize a Tikhonov functional which penalizes the gradient of the unknown function. Based on the resulting variational equation, we design an iteration method which is updated by solving a Poisson equation at each step. One-dimensional prototype examples illustrate the numerical performance of the proposed iteration.
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