Journal of Applied Analysis 06 (2000), No. 2, 187--212
Copyright Heldermann Verlag 2000
The Existence of Moments of Solutions to Transport Equations with Inelastic Scattering and Their Application in the Asymptotic Analysis
Jacek Banasiak
School of Mathematical and Statistical Sciences, University of Natal, Durban 4041, South Africa
We prove the existence of all moments of the solutions to the time-dependent spatially homogeneous transport equation describing elastic and inelastic scattering of particles. The proof uses the theory of resolvent positive operators and Desch's perturbation theorem. As an application we carry out the asymptotic analysis of the full transport equation with dominant elastic scattering and, using the results of the first part of the paper, we show that its solution can be approximated in the L1-norm by the solution of the limit equation obtained by formal asymptotic expansion.
Keywords: Evolution equations, positive semigroups, inelastic scattering, singular perturbations, hydrodynamic limit.
MSC: 34G10, 82C40, 47D06, 35Q35
[ Fulltext-pdf (251 KB)]