We consider a mixture composed of a gas and dust particles in a very rarefied setting. Whereas the dust particles are individually described, the surrounding gas is treated as a Knudsen gas, in such a way that interactions occur only between gas particles and dust by means of diffuse reflection phenomena. After introducing the model, we prove the existence and the uniqueness of the solution and provide a numerical strategy for the study of the equations. At the numerical level, we focus our attention on the phenomenon of energy transfer between the gas and the moving dust particles.

中文翻译：

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尘土努森混合气的数学和数值研究

我们考虑在非常稀疏的环境中由气体和灰尘颗粒组成的混合物。尽管分别描述了粉尘颗粒，但是将周围气体视为Knudsen气体，其方式是仅通过扩散反射现象在粉尘颗粒之间发生相互作用。引入模型后，我们证明了解的存在性和唯一性，并为方程的研究提供了数值策略。在数值层面上，我们将注意力集中在气体与移动的尘埃颗粒之间的能量转移现象上。