Abstract
We give an explicit solution of a model Boltzmann kinetic equation describing a gas between two walls maintained at different temperatures. In the model, which is essentially one-dimensional, there is a probability for collisions to reverse the velocities of particles traveling in opposite directions. Particle number and speeds (but not momentum) are collision invariants. The solution, which depends on the stochastic collision kernels at the walls, has a linear density profile and the energy flux satisfies Fourier's law.
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This paper is dedicated to Peter Gabriel Bergmann with affection and admiration on the occasion of his 70th birthday.
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Ianiro, N., Lebowitz, J.L. Stationary nonequilibrium solutions of model Boltzmann equation. Found Phys 15, 531–544 (1985). https://doi.org/10.1007/BF01882480
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DOI: https://doi.org/10.1007/BF01882480