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Mathematical Physics Seminar

On the Nonequilibrium steady state of dilute gases with thermal reservoirs

Eric Carlen - Rutgers University

Location:  Hill 705
Date & time: Thursday, 14 March 2019 at 2:00PM - 3:00PM

Abstract:  Study a kinetic model of a one-dimensional gas in contact with homogeneous thermal reservoirs at different temperatures. The interactions between particles is through collisions models by a BGK type of dynamics which conserves local energy and particle density. Weighting the nonlinear  BGK  term with a parameter \(alphain [0,1]\), and the interaction with the reservoirs by \((1-alpha)\), we prove that for some \(alpha_0>0\) and all \(alpha < alpha_0\), there are no spatially non-uniform non-equilibrium stationary states (NESS). We also show that for all \(alphain [0,1]\), the spatially uniform NESS, which is explicit, is  dynamically stable, with small perturbation converging to zero exponentially fast. Some extensions to higher dimensions are considered.

Joint work with R. Esposito,  J. Lebowitz,  R. Marra and C. Mouhot}