Existence and Uniqueness Theorems in the Inverse Problem of Recovering Surface Fluxes from Pointwise Measurements

Sergey Pyatkov and Denis Shilenkov
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Sergey Pyatkov: Institute of Digital Economics, Yugra State University, Chekhov St. 16, 628007 Khanty-Mansiysk, Russia
Denis Shilenkov: Institute of Digital Economics, Yugra State University, Chekhov St. 16, 628007 Khanty-Mansiysk, Russia

Mathematics, 2022, vol. 10, issue 9, 1-23

Abstract: Inverse problems of recovering surface fluxes on the boundary of a domain from pointwise observations are considered. Sharp conditions on the data ensuring existence and uniqueness of solutions in Sobolev classes are exposed. They are smoothness conditions on the data, geometric conditions on the location of measurement points, and the boundary of a domain. The proof relies on asymptotics of fundamental solutions to the corresponding elliptic problems and the Laplace transform. The inverse problem is reduced to a linear algebraic system with a nondegerate matrix.

Keywords: inverse problem; surface flux; convection-diffusion equation; heat and mass transfer; pointwise measurements (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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