Smoluchowski's discrete coagulation equation with forcing

TL;DR

This paper extends Smoluchowski's discrete coagulation equation to include particle input and output, demonstrating well-posedness and convergence to equilibrium with exponential rate under certain conditions.

Contribution

It introduces a new model incorporating particle forcing into the coagulation equation and proves its well-posedness and long-term behavior.

Findings

Model is well-posed for a broad class of kernels and rates.

Solutions converge exponentially to a unique equilibrium.

Long-time behavior is characterized under smallness conditions.

Abstract

In this article we study an extension of Smoluchowski's discrete coagulation equation, where particle in- and output takes place. This model is frequently used to describe aggregation processes in combination with sedimentation of clusters. More precisely, we show that the evolution equation is well-posed for a large class of coagulation kernels and output rates. Additionally, in the long-time limit we prove that solutions converge to a unique equilibrium with exponential rate under a suitable smallness condition on the coefficients.