Analytical Extensions of the Generalized Moment Method for the Smoluchowski Coagulation Equation

Abstract

This study extends the analytical framework of the generalized moment method for the Smoluchowski coagulation equation (SCE) to consider a wider range of kernels that can be associated with coagulation models, including those exhibiting complex growth behaviors. A key result of this work is the derivation of conditions under which the total mass of the system is conserved over time, even when the coagulation kernel is non-homogeneous. We provide two theorems along with their corresponding proofs to formalize the mentioned conditions.