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 elastic and inelastic scattering terms. 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 the physical point of View and allows to apply modifications of methods of the kinetic theory. Copyright (C) 2000 John Wiley & Sons, Ltd.