On the uniqueness of solution to the inverse problem of the atmospheric electricity

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Abstract

We investigate the inverse problem of determination of two unknown numerical parameters occuring linearly and nonlinearly in the higher coefficient of a linear second order elliptic equation of the diffusion-reaction type in a domain Ω diffeomorphic to a ball layer under special boundary conditions by observation in neighborhoods of the correspondent amount of points. For an analogous inverse problem under Dirichlet boundary conditions, sufficient conditions of solution uniqueness was obtained by the author formerly, but they had an abstract character and so were inconvenient for practical usage. In the paper, these conditions are extended to the case of different boundary conditions and rendered concrete for the case of the exponential type higher coefficient. The inverse problem investigated in the paper refers to research of electric processes in the Earth atmosphere in the frame of global electric circuit in the stationary approximation and arises from needs of recovering the unknown higher coefficient of the equation on the base of observation data obtained from two local transmitters.

About the authors

Andrei V. Chernov

National Research Lobachevsky State University of Nizhny Novgorod; Nizhny Novgorod State Technical University named after R.E. Alekseev

Email: chavnn@mail.ru
Candidate of Physics and Mathematics, Associate Professor of the Applied Mathematics Department 23 Gagarin Ave., Nizhni Novgorod 603950, Russian Federation; 24 Minin St., Nizhni Novgorod 603950, Russian Federation

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