Propagation of Chaos for a Thermostated Kinetic Model
| Autor: | Bonetto, F., Carlen, E. A., Esposito, R., Lebowitz, J. L., Marra, R. |
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| Rok vydání: | 2013 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s10955-013-0861-2 |
| Popis: | We consider a system of N point particles moving on a d-dimensional torus. Each particle is subject to a uniform field E and random speed conserving collisions. This model is a variant of the Drude-Lorentz model of electrical conduction. In order to avoid heating by the external field, the particles also interact with a Gaussian thermostat which keeps the total kinetic energy of the system constant. The thermostat induces a mean-field type of interaction between the particles. Here we prove that, starting from a product measure, in the large N limit, the one particle velocity distribution satisfies a self consistent Vlasov-Boltzmann equation.. This is a consequence of "propagation of chaos", which we also prove for this model. Comment: This version adds affiliation and grant information; otherwise it is unchanged |
| Databáze: | arXiv |
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