On the hydrodynamic closure of a transport-diffusion equationM. Bisi1, G. Spiga1 and G. Toscani2
1 Dipartimento di Matematica, Università di Parma - Viale G. P. Usberti 53/A, 43100 Parma, Italy, EU
2 Dipartimento di Matematica, Università di Pavia - Via Ferrata 1, 27100 Pavia, Italy, EU
received 7 May 2008; accepted in final form 5 July 2008; published August 2008
published online 19 August 2008
In this paper we discuss the passage to hydrodynamics for a transport diffusion equation. It is shown that the self-similar solution of the diffusion equation can be fruitfully used to construct the Euler equations for the model, provided the initial density possesses sufficiently many moments. The results of the paper can be of interest in dissipative kinetic theory, where the role of the homogeneous cooling state in the passage to hydrodynamics has been shown only from a formal point of view.
05.60.-k - Transport processes.
05.20.Dd - Kinetic theory.
02.30.Jr - Partial differential equations.
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