G. L. CARAFFINI, C. E. CATALANO and G. SPIGA
On the small mean free path asymptotics of the transport equation with inelastic scattering
Received: 7 April 1998
Mathematics Subject Classification (2000): 82C40 - 76P05
Abstract: The asymptotic analysis of the linear Boltzmann equation with inelastic scattering is performed with respect to the proper Knudsen number for three physical situations characterized by different mutual relationships between elastic and inelastic collision terms and by negligible up-scattering. After establishing all necessary mathematical properties, the compressed asymptotic method by Mika and Banasiak is used to derive the first order approximate limiting equation, which does not always turn out to be of diffusive type.