In the last few decades 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 suggest a model of the Nazi Germany invasion of Poland, France, and the USSR based on kinetic theory. We simulate this process with the Cauchy boundary problem for two-element kinetic equations. The solution of the problem is given in the form of a traveling wave. The propagation velocity of a front line depends on the quotient between initial forces concentrations. Moreover it is obtained that the general solution of the model can be expressed in terms of quadratures and elementary functions. Finally it is shown that the front-line velocities agree with the historical data.

• Received 14 December 2014

DOI:https://doi.org/10.1103/PhysRevE.91.042806