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