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Boltzmann asymptotics with diffuse reflection boundary conditions. (English) Zbl 0877.76063
This paper deals with the nonlinear Boltzmann equation $$(\partial_t+ \xi \cdot \nabla_x) f=Q(f,f)$$, where $$Q$$ is the collision operator. The collisionless case is first considered, and then strong $$L^1$$-convergence to a stationary solution when $$t\to+ \infty$$ is proved in a bounded domain, with constant temperature on the boundary.

MSC:
 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics 82B40 Kinetic theory of gases in equilibrium statistical mechanics 45K05 Integro-partial differential equations
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References:
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