\(L^1\) solutions to the stationary Boltzmann equation in a slab. (English) Zbl 0991.45005
Summary: The stationary Boltzmann equation for pseudo-Maxwellian and hard forces is considered in the slab. An \(L^1\) existence theorem is proven in the case of diffuse reflection boundary conditions. The method of proof is based on properties of the entropy dissipation term. The approach is simplified by a classical transformation of the space variable resulting in a homogeneous equation of degree one. The case of given indata is also briefly discussed.
MSC:
| 45K05 | Integro-partial differential equations |
| 82C40 | Kinetic theory of gases in time-dependent statistical mechanics |
Keywords:
stationary Boltzmann equation; existence; diffuse reflection boundary conditions; entropy dissipationReferences:
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