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Existence of a
nonequilibrium steady state for the nonlinear BGK equation on
an interval
Josephine Evans and Angeliki Menegaki |
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Vol. 3 (2021), No. 1, 223–252
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Abstract |
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We show existence of a nonequilibrium steady state for the one-dimensional, nonlinear BGK model on an interval with diffusive boundary conditions. These boundary conditions represent the coupling of the system with two heat reservoirs at different temperatures. The result holds when the boundary temperatures at the two ends are away from the equilibrium case, as our analysis is not perturbative around the equilibrium. We employ a fixed point argument to reduce the study of the model with nonlinear collisional interactions to the linear BGK model. |
Keywords
nonequilibrium steady state, nonlinear BGK model, diffusive
boundary conditions, existence results, heat transfer
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Mathematical Subject Classification
Primary: 35Q20, 35Q49, 35Q82
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Milestones
Received: 10 August 2020
Revised: 5 October 2020
Accepted: 19 January 2021
Published: 28 May 2021
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Authors |
| Josephine Evans | |
| Warwick Mathematics Institute University of Warwick Coventry United Kingdom |
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| Angeliki Menegaki | |
| Department of Pure Mathematics and
Mathematical Statistics Centre for Mathematical Sciences University of Cambridge United Kingdom |
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