American Institute of Mathematical Sciences

September  2019, 9(3): 509-515. doi: 10.3934/mcrf.2019023

Determining the shape of a solid of revolution

 Department of Mathematics, University of West Georgia, Carrollton, GA 30118, USA

Received  June 2017 Revised  May 2018 Published  April 2019

We show how to reconstruct the shape of a solid of revolution by measuring its temperature on the boundary. This inverse problem reduces to finding a coefficient of a parabolic equation from values of the trace of its solution on the boundary. This is achieved by using the inverse spectral theory of the string, as developed by M.G. Krein, which provides uniqueness and also a reconstruction algorithm.

Citation: Amin Boumenir. Determining the shape of a solid of revolution. Mathematical Control & Related Fields, 2019, 9 (3) : 509-515. doi: 10.3934/mcrf.2019023
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