The global attractor of the inelastic linear Boltzmann equation in a gravity field for Maxwell molecules
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916996749197312 |
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| author | Dolmaire, Théophile Miele, Nicola Nota, Alessia |
| author_facet | Dolmaire, Théophile Miele, Nicola Nota, Alessia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02155 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The global attractor of the inelastic linear Boltzmann equation in a gravity field for Maxwell molecules Dolmaire, Théophile Miele, Nicola Nota, Alessia Analysis of PDEs Mathematical Physics 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. |
| title | The global attractor of the inelastic linear Boltzmann equation in a gravity field for Maxwell molecules |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2504.02155 |