This article is cited in 3 papers

MODELS OF ECONOMIC AND SOCIAL SYSTEMS

Description of the rapid invasion processes by means of the kinetic model

V. V. Aristov, O. V. Ilyin

Dorodnicyn Computing Centre of Russian Academy of Sciences, 40 Vavilova str., Moscow, 119333, Russia

Abstract: Recently many investigations have been devoted to theoretical models in new areas concerning description of different biological, sociological and historical processes. In the present paper we investigate the nazi Germany invasion in Poland, France and USSR from the kinetic theory point of view. We model this process with the Cauchy boundary problem for the two-element kinetic equations with spatial uniform initial conditions. The solution of the problem is given in the form of the traveling wave and the propagation velocity of a frontline depends on the quotient between initial forces concentrations. Moreover it is obtained that the general solution of the model can be obtained in terms of the quadratures and elementary functions. Finally it is shown that the frontline velocities are complied with the historical data.

Keywords: kinetic theory, models of aggression.

UDC: 533.6.011

Received: 03.05.2014
Revised: 09.07.2014

DOI: 10.20537/2076-7633-2014-6-5-829-838