Inverse Problems for the Diffusion–Drift Model of Charging of an Inhomogeneous Polar Dielectric

The problems of reconstructing the unknown parameters of the model of electron-induced charging of an inhomogeneous polar dielectric from additional information about the volume charge density distribution and the electric field strength are studied. Within the optimization approach, these inverse p...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2023-09, Vol.63 (9), p.1685-1699
Main Authors: Brizitskii, R. V., Maksimova, N. N., Maslovskaya, A. G.
Format: Article
Language:English
Subjects:
Boundary value problems
Charge density
Charging
Computational Mathematics and Numerical Analysis
Density distribution
Electric field strength
Inhomogeneity
Inverse problems
Mathematical Physics
Mathematics
Mathematics and Statistics
Optimization
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Summary:The problems of reconstructing the unknown parameters of the model of electron-induced charging of an inhomogeneous polar dielectric from additional information about the volume charge density distribution and the electric field strength are studied. Within the optimization approach, these inverse problems are reduced to control problems and their solvability is proved. For extremum problems, optimality systems are derived and, based on their analysis, local uniqueness of the solution of one of the considered problems is proved. Taking into account the introduced characteristic of the inhomogeneity of the dielectric, auxiliary results on the solvability and properties of solutions of the boundary value problem, obtained earlier for the model of charging of a homogeneous dielectric, are corrected.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542523090051