STRUCTURAL STABILITY OF THE COALESCENCE BREAKUP EQUATION

An analysis of the structural stability of the coalescence/breakup equ ation is performed to determine the degree to which changes in the equ ation's formulation can affect the solution. The work was motivated by speculation in various quarters that the currently used coalescence/b reakup formulation should be adjusted to achieve better agreement betw een solutions and field observations. Both analytical procedures and n umerical experiments, in which hypothetical changes in the rate coeffi cients are assumed, show the coalescence/breakup equation in its curre nt formulation to be structurally stable. Not only do small changes in the rate coefficients produce negligible change in the solutions, but even large changes in the rate coefficients fail to destroy the funda mental behavior of the system in that all solutions continue to approa ch a unique equilibrium. Moderate-sized perturbations of the coefficie nts are found to have only minor influence on the solutions unless the coalescence and breakup efficiencies, constituents of the rate coeffi cients, are perturbed in an opposite sense to reinforce the individual effects. Only with such changes in the formulation is the equilibrium solution found to be altered to a significant degree.