Fast fusion in a two-dimensional coagulation model

Abstract

In this work, we study a particular system of coagulation equations characterized by two values, namely volume v and surface area a. Compared to the standard one-dimensional models, this model incorporates additional information about the geometry of the particles. We describe the coagulation process as a combination between collision and fusion of particles. We prove that we are able to recover the standard one-dimensional coagulation model when fusion happens quickly and that we are able to recover an equation in which particles interact and form a ramified like system in time when fusion happens slowly.