Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

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. Preprints 2022, 2022040102 (doi: 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 (doi: 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

MATHEMATICS & COMPUTER SCIENCE, General Mathematics

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