ON A REGULARIZED SYSTEM OF SELF-GRAVITATING PARTICLES

We consider a regularized macroscopic model describing a system of self-gravitating particles. We study the existence and uniqueness of non-negative stationary solutions and allude the differences to results obtained from classical gravitational models. The system is analyzed on a convex, bounded domain up to three spatial dimensions, subject to Neumann boundary conditions for the particle density, and Dirichlet boundary condition for the self-interacting potential. Finally, we show numerical simulations underlining our analytical results.