Expansion into vacuum of a gaseous ellipsoid with repulsion between the particles

Methods of the analytic theory of differential equations as well as the numerical methods are used to study the problem of adiabatic expansion of a homogeneous cloud of perfect gas into vacuum. The Cartesian and Lagrangian coordinates of the gas particles are connected by a linear relation, and the particles have a charge which generates a macroscopic field within the cloud, without however affecting the properties of the perfect gas.