On the particle approximation to stationary solutions of the Boltzmann equation

Mario Pulvirenti; Mario Pulvirenti

doi:10.3934/mine.2019.4.699

Mathematics in Engineering

2019, Volume 1, Issue 4: 699-714. doi: 10.3934/mine.2019.4.699

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On the particle approximation to stationary solutions of the Boltzmann equation

Mario Pulvirenti ^{1,2
,
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1.
Dipartimento di Matematica, Università di Roma La Sapienza Piazzale Aldo Moro 5, 00185 Roma–Italy
2.
International Research Center M&MOCS, Università dell’Aquila, Palazzo Caetani, Cisterna di Latina, (LT) 04012 Italy.

Received: 26 January 2019 Accepted: 24 July 2019 Published: 14 August 2019

We discuss the problem of the approximation of the solutions of the stationary Boltzmann equation, driven by diffuse boundary conditions at varying temperature, by means of stochastic particle systems. In particular we extend a previous results, by substituting the hypothesis of a cutoff on small and large velocities with the presence of an external field.
- Boltzmann equation,
- particle approximation,
- scaling limits
Citation: Mario Pulvirenti. On the particle approximation to stationary solutions of the Boltzmann equation[J]. Mathematics in Engineering, 2019, 1(4): 699-714. doi: 10.3934/mine.2019.4.699

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Abstract

We discuss the problem of the approximation of the solutions of the stationary Boltzmann equation, driven by diffuse boundary conditions at varying temperature, by means of stochastic particle systems. In particular we extend a previous results, by substituting the hypothesis of a cutoff on small and large velocities with the presence of an external field.

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