In this paper, a complete analytical solution to the
integro-differential model describing the nucleation and growth of
ellipsoidal crystals in a supersaturated solution is obtained. The
asymptotic solution of the model equations is constructed using the
saddle-point method to evaluate the Laplace-type integral. Numerical
simulations carried out for physical parameters of real solutions show
that the first four terms of the asymptotic series give a convergent
solution. The developed theory was compared with the experimental data
on desupersaturation kinetics in proteins. It is shown that the theory
and experiments are in good agreement.