ИСТИНА

We consider the gravitating particles that can collide. Collisions can be described in various ways. We can use the theory of inelastic interaction of solids with Newton’s recovery coefficient for the relative velocity of colliding particles. In numerical implementation, the main difficulty of this approach is to track and refine a huge number of time moments of particle collisions. Another approach is to add to the gravitational potential the potential of repulsive forces, similar to the intermolecular Lennard-Jones forces. Numerical experiments show that when the Jacobi stability condition is satisfied, both models lead to a qualitatively identical character of evolution with the possible formation of stable configurations. As it is known, when pair collisions of an infinitely large number of gravitating particles are taken into account, the probability density function evolves in accordance with the Vlasov-Boltzmann-Poisson system of equations. We suggest a research method using the Vlasov equation with the Lennard-Jones type potential. This allows to take into account the size of the interacting particles, and also take into account not only paired, but also triple or more collisions of the particles. For this dynamical system the existence of a large class of nonlinearly stable equilibrium solutions is proved by the Energy-Casimir method.