Abstract :

We propose a model based on the coupling of two Boltzmann-like equations for the study of the evolution of dust particles in a rarefied atmosphere, such as it can be found in the context of safety studies for the ITER project of nuclear fusion. When the typical size of a dust speck becomes too large, the numerical simulation of the system under study becomes too expensive and one needs to introduce an asymptotic model in which the mass ratio between molecules and dust speck tends to 0. This model is constituted of a coupling (by a drag force term) between a Boltzmann equation and a Vlasov equation. A rigorous proof of the passage to the limit is given in the spatially homogeneous setting. It includes a new variant of Povzner's inequality in which the vanishing mass ratio is taken into account.