Parabolic systems of "reaction-diffusion" type in case of modeling the processes of generation and propagation of electromagnetic emission of lithosphere
and methods of their analysis
© I.M. Tsyfra, V.N. Shuman
The problems of generation within geo-medium of electromagnetic disturbances of radio-wave (kilo-hertz) region registered on the Earth's surface are considered in the paper. Attention is concentrated on mathematical aspects of the problem, namely on the analysis of earlier proposed non-linear equation of generation of the type "reaction-diffusion" which gives a description of the complicated excitation regimes and propagation of electromagnetic disturbances in the considered model of geo-medium - self-similar structure, which determines seismic and electromagnetic processes in it. Review is given on the physical level, and peculiarities of this equation are analyzed and possible ways of its solution. In order to simplify the equation under analysis it is proposed in the work to use its symmetry. Symmetry method allows reducing the equations (or their system) in partial derivatives of parabolic type to the study of a system of ordinary differential equations. For this purpose both classical theory-group approach and its generalization - conditional invariance method can be used.