Mathematical and numerical study of a kinetic model describing the evolution of planetary rings

In this paper, we study a kinetic model describing the evolution of planetary dust under the action of a planet and its satellites. In particular, we focus our attention on the formation of planetary rings and the role of shepherd moons. The equation describing the considered physical phenomenon is of Vlasov type, posed in an evolutionary domain in time. We first study some theoretical properties of the model. Then, we describe a numerical method, suitable for the study of kinetic equations in evolutionary domains with possibly complicated geometries. Finally, we show and comment some simulations. In particular, our numerical simulations show that shepherd moons play a key role in the formation and maintenance of divisions between rings.