ASYMPTOTIC ANALYSIS FOR A PARTICLE TRANSPORT EQUATION WITH INELASTIC SCATTERING IN EXTENDED KINETIC THEORY

Author:

BANASIAK JACEK1,FROSALI GIOVANNI2,SPIGA GIAMPIERO3

Affiliation:

1. Department of Mathematics, University of Natal, Durban 4001, South Africa

2. Dipartimento di Matematica "V.Volterra", Università di Ancona, Via Brecce Bianche, I-60131 Ancona, Italy

3. Dipartimento di Matematica, Università di Parma, Via M. D'Azeglio 85, I-43100 Parma, Italy

Abstract

In this paper we perform the asymptotic analysis for a linear transport equation for test particles in an absorbing and inelastically scattering background, when the excited species can be considered as non-participating. This model is derived in the frame of extended kinetic theory and rescaled with the Knudsen number ∊. After examining the main properties of the collision model and of the scattering operator in the case with an infinite interval of energy as well as the case with a finite interval, the modified (compressed) Chapman–Enskog expansion procedure is applied to find the asymptotic equation for small mean free path. A specific feature of this model is that the collision operator has an infinite-dimensional null-space. The main result is that in the small mean free path approximation on [Formula: see text] level we obtain a free molecular flow for a suitable hydrodynamic quantity, rather than the diffusion which is typical for linear transport problems.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

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