On a diffusion-kinetic equation arising in extended kinetic theory

This paper is devoted to the study of solvability of an evolution equation obtained as a hydrodynamic limit of a linear Boltzmann equation with elasti c and inelastic scattering terms. An interesting feature of this equation i s that it combines the diffusion operator and a singular operator of a kine tic type. The study is carried out in the L-1 space which is natural from t he physical point of View and allows to apply modifications of methods of t he kinetic theory. Copyright (C) 2000 John Wiley & Sons, Ltd.