Oscillatory processes in the theory of particulate formation in supersaturated chemical solutions

We study a nonlinear problem which occurs in the theory of particulate formation in supersaturated chemical solutions. Mathematically, the problem involves the bifurcation of time-periodic solutions in an initial-boundary value problem involving a nonlinear integro-differential equation. The mechanism controlling the oscillatory states is revealed by combining the theory of characteristics for first order partial differential equations with the multi-time scale perturbation analysis of a certain third order system of nonlinear ordinary differential equations.