FEATURES OF MATHEMATICAL MODELING IN THE GROUND LAYER ELECTRODYNAMICS
Abstract
The paper examines the problem of integrating the system of electrodynamic equations of
the atmosphere surface layer for various cases of the electrode effect. The original system of differential
equations of the electrode effect is reduced to the so-called total current equation, which
is a second-order equation of parabolic type, considered in a two-dimensional space-time region.
The total current equation allows us to relate the set of main factors influencing the state of the
electric field in the atmosphere surface layer: conduction current, turbulent current and current
arising as a result of convective processes in the atmosphere with the so-called total current in the
surface layer, reflecting changes in the potential of the ionosphere. The described method provides
significant advantages in the study, since within the framework of one model it allows the formulation
of various problems of the surface layer electrodynamics and a comparative analysis of the
influence of both individual factors and their combinations on the behavior of the electric field in
the surface layer. The purpose of the work is to analyze the mathematical aspects of the models
under consideration from the point of view of approaches to integrating the total current equation.
The study compares the features of physical formulations and their influence on the structure of
mathematical models and their properties from the point of view of mathematical physics. The
various physical formulations considered show that even in a relatively simple mathematical model
consisting of one equation supplemented with initial boundary conditions, a fairly wide range of
both model formulations and approaches to integrating the considered models arises.
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