Existence of solutions of a kinetic equation modeling cometary flows

A global existence theorem is presented for a kinetic problem of the form ?tf + ?ž ?xf = Q(f), f(t=0) = f0, where Q(f) is a simplified model wave particle collision operator extracted from quasilinear plasma physics. Evaluation of Q(f) requires the computation of the mean velocity of the distribution f. Therefore, the assumptions on the data are such that vacuum regions, where the mean velocity is not well defined, are excluded. Also the initial data are assumed to have bounded total energy. As additional results conservation laws for mass, momentum, and energy are derived, as well as an entropy dissipation law and the propagation of higher order moments.