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arXiv · 2504.02155

The global attractor of the inelastic linear Boltzmann equation in a gravity field for Maxwell molecules

Théophile Dolmaire·Nicola Miele·Alessia Nota
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Abstract

In this article we consider the linear inelastic Boltzmann equation in presence of a uniform and fixed gravity field, in the case of Maxwell molecules. We first obtain a well-posedness result in the space of finite, non-negative Radon measures. In addition, we rigorously prove the existence of a stationary solution under the non-equilibrium condition which is induced by the presence of the external field. We further show that this stationary solution is unique in the class of the finite, non-negative Radon measures with finite first order moment, and that all the solutions in this class converge towards the stationary solution in the weak topology of the measures.

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Théophile Dolmaire, Nicola Miele, Alessia Nota. 2025-04-02. The global attractor of the inelastic linear Boltzmann equation in a gravity field for Maxwell molecules. https://arxiv.org/abs/2504.02155

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