Version 1
: Received: 8 April 2022 / Approved: 11 April 2022 / Online: 11 April 2022 (14:24:26 CEST)
How to cite:
Pyatkov, S.G.; Shilenkov, D. Existence and Uniqueness Theorems in the Inverse Problem of Recovering Surface Fluxes from Pointwise Measurements. Preprints2022, 2022040102. https://doi.org/10.20944/preprints202204.0102.v1
Pyatkov, S.G.; Shilenkov, D. Existence and Uniqueness Theorems in the Inverse Problem of Recovering Surface Fluxes from Pointwise Measurements. Preprints 2022, 2022040102. https://doi.org/10.20944/preprints202204.0102.v1
Pyatkov, S.G.; Shilenkov, D. Existence and Uniqueness Theorems in the Inverse Problem of Recovering Surface Fluxes from Pointwise Measurements. Preprints2022, 2022040102. https://doi.org/10.20944/preprints202204.0102.v1
APA Style
Pyatkov, S.G., & Shilenkov, D. (2022). Existence and Uniqueness Theorems in the Inverse Problem of Recovering Surface Fluxes from Pointwise Measurements. Preprints. https://doi.org/10.20944/preprints202204.0102.v1
Chicago/Turabian Style
Pyatkov, S.G. and Denis Shilenkov. 2022 "Existence and Uniqueness Theorems in the Inverse Problem of Recovering Surface Fluxes from Pointwise Measurements" Preprints. https://doi.org/10.20944/preprints202204.0102.v1
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 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
Subject
Computer Science and Mathematics, Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
