We present a non-stationary growth model of Ga-catalyzed GaAs nanowires which is based on the two kinetic equations for the nanowire elongation rate and a time-dependent base radius of the droplet. We show that self-catalyzed nanowire growth is principally different from the Au-catalyzed one because a stationary droplet size cannot be maintained at all times. Close examination of the model enables us to separate different regimes of radial growth in which the droplet shrinks, inflates or converges to a certain stationary size as nanowires grow, depending on the initial droplet radius and the growth conditions. We also discuss some experimental data on the growth modes of Ga-catalyzed GaAs nanowires from the viewpoint of the obtained results.