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Bifurcation on boundary data for linear Broadwell model with conservative boundary condition. (English) Zbl 1304.82064

Summary: We study a simple kinetic model with a conservative boundary condition which resembles the Maxwell diffuse boundary condition for the Boltzmann equation. We use a streamlined approach to construct the global pointwise structure of the full boundary data from the imposed boundary condition. Our estimates are strong enough to conclude the bifurcation in terms of the coefficients of the Broadwell model and the speed of the physical boundary.

MSC:

82C40 Kinetic theory of gases in time-dependent statistical mechanics
35Q20 Boltzmann equations
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[1] DOI: 10.1002/cpa.3160320404 · Zbl 0387.76068 · doi:10.1002/cpa.3160320404
[2] DOI: 10.1007/BF01218291 · Zbl 0665.76089 · doi:10.1007/BF01218291
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