Instantaneous gelation in Smoluchowski's coagulation equation revisited.

We study the solutions of the Smoluchowski coagulation equation with a regularization term which removes clusters from the system when their mass exceeds a specified cutoff size, M. We focus primarily on collision kernels which would exhibit an instantaneous gelation transition in the absence of any regularization. Numerical simulations demonstrate that for such kernels with monodisperse initial data, the regularized gelation time decreases as M increases, consistent with the expectation that the gelation time is zero in the unregularized system.