Existence of solutions of a kinetic equation modeling cometary flows

A global existence theorem is presented for a kinetic problem of the form p artial derivative(t)f + upsilon.del(x)f = Q(f), f(t = 0) = f(0), where Q(f) is a simplified model wave-particle collision operator extracted from quas ilinear plasma physics. Evaluation of P(f) requires the computation of the mean velocity of the distribution f. Therefore, the: assumptions on the dat a 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 ene rgy. 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.