No abstract

Communicated by M. Lachowicz SUMMARY A discrete version of the Oort-Hulst-Safronov (OHS) coagulation equation is studied. Besides the existence of a solution to the Cauchy problem, it is shown that solutions to a suitable sequence of those discrete equations converge towards a solution to the OHS equation.

We show the existence of a self-similar solution for a modified Boltzmann equation describing probabilistic ballistic annihilation. Such a model describes a system of hard spheres such that, whenever two particles meet, they either annihilate with probability α ∈ (0, 1) or they undergo an elastic collision with probability 1 − α. For such a model, the number of particles, the linear momentum and the kinetic energy are not conserved. We show that, for α smaller than some explicit threshold value α1, a self-similar solution exists.

We study the Cauchy problem for the spatially homogeneous Landau equation for Fermi–Dirac particles, in the case of hard and Maxwellian potentials. We establish existence and uniqueness of a weak solution for a large class of initial data.