The Boltzmann equation with non-isothermal Maxwell boundary conditions

Key Points

• The aim is to investigate the Boltzmann equation near the hydrodynamic limit, focusing on non-isothermal conditions.
• Analyzed the Boltzmann equation in bounded spatial domains
• Applied non-isothermal Maxwell boundary conditions
• Established criteria for existence and uniqueness of steady states
• Examined asymptotic stability under temperature fluctuation assumptions
• Found the existence of a non-equilibrium steady state under certain conditions
• Demonstrated uniqueness of the steady state in the studied regime
• Confirmed asymptotic stability of the steady state against temperature fluctuations