Convergence to equilibrium for a class of coagulation-fragmentation equations without detailed balance

TL;DR

This paper establishes convergence to equilibrium for certain coagulation-fragmentation equations lacking detailed balance, providing explicit rates and proving uniqueness of stationary states for perturbations of constant rate kernels.

Contribution

It introduces a novel analysis of coagulation-fragmentation equations without detailed balance, including explicit convergence rates and uniqueness results.

Findings

Proves convergence to equilibrium for a class of coagulation-fragmentation equations.

Provides explicit rates of convergence.

Establishes uniqueness of stationary states.

Abstract

We prove convergence to equilibrium for a class of coagulation-fragmentation equations that do not satisfy a detailed balance condition. More precisely, we consider perturbations of constant rate kernels. Our result provides in particular explicit convergence rates. Uniqueness of the stationary states is proven as well for the considered class of kernels.