This is the abstract of the paper
  "The existence of moments of solutions to transport equations with
   inelastic scattering and their application in the asymptotic analysis"
by J. Banasiak.

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Abstract: In this paper we prove the existence of all  moments of
solutions to the time-depended spatially homogeneous transport equation
describing elastic and inelastic scattering of particles. The proof uses
Arendt-Batty-Robinson generation theorem for resolvent positive
operators.  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 $L_1$-norm by the solution of
the limit equation obtained by formal asymptotic expansion

Key words:  evolution equations, positive semigroups,
            inelastic scattering, singular perturbations,
            hydrodynamic limit

AMS Subject Classification  34G10, 82C40, 47D06, 35Q35