Abstract
A simple idea of finding a domain that encloses an unknown discontinuity embedded in a body is introduced by considering an inverse boundary value problem for the heat equation. The idea gives a design of a special heat flux on the surface of the body such that from the corresponding temperature field on the surface one can extract the smallest radius of the sphere centered at an arbitrary given point in the whole space and enclosing unknown inclusions. Unlike before, the designed flux is free from a large parameter. An application of the idea to a coupled system of the elastic wave and heat equations are also given.
Funding source: Japan Society for the Promotion of Science
Award Identifier / Grant number: 17K05331
Award Identifier / Grant number: 18H01126
Funding statement: The author was partially supported by Grant-in-Aid for Scientific Research (C) (No. 17K05331) and (B) (No. 18H01126) of Japan Society for the Promotion of Science.
Acknowledgements
Some of this work was started by the author during his visit to University of Helsinki in March 2019. The author would like to thank Samuli Siltanen for having useful discussions during the stay.
References
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