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.