On solutions of the Lifshitz-Slyozov model

We derive global existence and uniqueness of solutions for the Lifshitz-Slyozov system, which appears in the modelling of precipitation from supersaturated solutions. Mathematically, the system consists of a transport equation for the density function, coupled to an integral equation which expresses conservation of the total mass. The existence is obtained by a fixed-point technique, based on the expression of the density function in terms of the monomer concentration, as given by the method of characteristics. For some particular cases we obtain an explicit expression of the solution by using the Laplace transform. Finally, in some more general cases, we prove, if a solution exists, convergence to a stationary solution for large times. AMS classification scheme numbers: 35, 82.