Abstract
In this article, we consider a general second-order hyperbolic equation. We first establish a modified Carleman estimate for this equation by adding some functions of adjustment. Then general conditions imposed on the principal parts, mixed with the weight function and the functions of adjustment are derived. Finally, we give the realizations of the weight functions by choosing suitable adjustments such that the above general conditions are satisfied in some specific cases.
Dedicated to Masahiro Yamamoto Sensei for His Sixtieth Birthday.
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Acknowledgements
The author is supported by Grant-in-Aid for Scientific Research(S) 15H05740 of Japan Society for the Promotion of Science (JSPS). This work is also supported by A3 Foresight Program “Modeling and Computation of Applied Inverse Problems” of JSPS.
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Huang, X. (2020). Carleman Estimate for a General Second-Order Hyperbolic Equation. In: Cheng, J., Lu, S., Yamamoto, M. (eds) Inverse Problems and Related Topics. ICIP2 2018. Springer Proceedings in Mathematics & Statistics, vol 310. Springer, Singapore. https://doi.org/10.1007/978-981-15-1592-7_7
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DOI: https://doi.org/10.1007/978-981-15-1592-7_7
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