For small values of the nonlinear parameter alpha, a kinetic Fokker-Planck equation with BGK thermostats and space-dependent Maxwell boundary conditions admits an exponentially stable non-equilibrium steady state.
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Existence and stability of non-equilibrium steady states of a weakly non-linear kinetic Fokker-Planck equation in a domain
For small values of the nonlinear parameter alpha, a kinetic Fokker-Planck equation with BGK thermostats and space-dependent Maxwell boundary conditions admits an exponentially stable non-equilibrium steady state.