ON THE SOLUTION OF THE COAGULATION EQUATION WITH A TIME-DEPENDENT SOURCE-APPLICATION TO PULSED INJECTION

A general theoretical treatment is developed for the solution of the t ime-dependent coagulation equation (with constant coagulation kernel) in the presence of a source term possessing arbitrary time dependence. It is shown how the relevant nonlinear first-order differential equat ion can be transformed into a linear second-order equation, which can then be used to obtain the general solution of the problem together wi th information about its asymptotic long-term behaviour. The technique is applied to a periodic source term where it is found that the long- term behaviour of the solution exhibits the same periodicity as the so urce. Detailed results are derived for particular source terms.