A class of growth and bounds to solutions of a differential equation.
Under suitable hypotheses on , , we prove some stability results which relate the asymptotic behavior of the solutions of to the asymptotic behavior of the solutions of .
A stochastic system of particles is considered in which the sizes of the particles increase by successive binary mergers with the constraint that each coagulation event involves a particle with minimal size. Convergence of a suitably renormalized version of this process to a deterministic hydrodynamical limit is shown and the time evolution of the minimal size is studied for both deterministic and stochastic models.