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Measure Solutions for the Steady Nonlinear Boltzmann Equation in a Slab

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Abstract:

We prove that the Boltzmann equation in a slab, with boundary conditions of diffuse reflection and mass conservation at the wall and assigned total mass (per unit area) in a slab has at least one non-negative measure-valued solution. The physical model is provided by Maxwellian molecules with angular cutoff. The equation is rewritten after a change of variables which is shown to be invertible.

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  1. Dipartimento di Matematica, Politecnico di Milano, I–20133 Milano, Italy, , , , , , IT

    Carlo Cercignani

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  1. Carlo Cercignani
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Received: 22 January 1997 / Accepted: 6 March 1998

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Cercignani, C. Measure Solutions for the Steady Nonlinear Boltzmann Equation in a Slab . Comm Math Phys 197, 199–210 (1998). https://doi.org/10.1007/s002200050447

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  • DOI: https://doi.org/10.1007/s002200050447

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