Multicomponent coagulation systems: existence and non-existence of stationary non-equilibrium solutions

TL;DR

This paper investigates the existence of stationary solutions in multicomponent coagulation systems described by the Smoluchowski equation, extending previous one-component results to classify when such solutions exist or not under non-equilibrium conditions.

Contribution

It generalizes the analysis of stationary solutions from one-component to multicomponent systems with general kernels, providing new criteria for existence and non-existence.

Findings

Classifies parameter ranges for solution existence.

Provides criteria for constant mass flux solutions.

Extends previous one-component coagulation results.

Abstract

We study multicomponent coagulation via the Smoluchowski coagulation equation under non-equilibrium stationary conditions induced by a source of small clusters. The coagulation kernel can be very general, merely satisfying certain power law asymptotic bounds in terms of the total number of monomers in a cluster. The bounds are characterized by two parameters and we extend previous results for one-component systems to classify the parameter values for which the above stationary solutions do or do not exist. Moreover, we also obtain criteria for the existence or non-existence of solutions which yield a constant flux of mass towards large clusters.