This is the abstract of the paper
  "On a diffusion-kinetic equation arising in extended kinetic theory"
by Jacek Banasiak.

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Abstract: The paper is devoted to the study of solvability of an evolution
equation obtained as a hydrodynamic limit of  a linear Boltzmann
equation with inelastic scattering term.
An interesting feature of this equation is that it combines
the diffusion operator  and a singular operator of a kinetic type.
The study is carried out in the $L_1$ space
which is natural from physical point of view and allows to
use an adaptation of Arlotti's generalization of Miyadera-Voigt
perturbation theorem.

Key words:  evolution equations, positive semigroups, inelastic
            scattering, singular perturbations, diffus~ion approximation

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