Remarks on the Theorem for a non involutive Boltzmann like kinetic model
Giulia Furioli
Università di Bergamo, Dalmine, ItalyElide Terraneo
Università degli Studi di Milano, Italy
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Abstract
In this paper, we consider a one-dimensional kinetic equation of Boltzmann type in which the binary collision process is described by the linear transformation , , where are the pre-collisional velocities and the post-collisional ones and are two positive parameters. This kind of model has been extensively studied by Pareschi and Toscani (in J. Stat. Phys., 124(2–4):747–779, 2006) with respect to the asymptotic behavior of the solutions in a Fourier metric. In the conservative case , even if the transformation has Jacobian and so it is not involutive, we remark that the Theorem holds true. As a consequence we prove exponential convergence in of the solution to the stationary state, which is the Maxwellian.
Cite this article
Giulia Furioli, Elide Terraneo, Remarks on the Theorem for a non involutive Boltzmann like kinetic model. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 21 (2010), no. 2, pp. 193–213
DOI 10.4171/RLM/567