The specular reflective boundary problem for the Boltzmann equation with soft potentials
Journal article, Peer reviewed
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Original versionNonlinear Analysis. 2012, 75 786-805. 10.1016/j.na.2011.09.011
In this paper, we consider the specular reflective boundary problem for the onedimensional Boltzmann equation with soft potentials. It is shown that the solution converges to a global Maxwellian M+ under certain initial conditions. In order to prove this, we construct a local Maxwellian M¯ which is very close to M+ as an ansatz of M and obtain the stability of M¯ . Our proof is based on elementary energy estimates and detailed properties of Burnett functions.