The Redner-ben-Avraham-Kahng cluster system without growth condition on the kinetic coefficients

TL;DR

This paper proves the existence of global solutions for the Redner-ben-Avraham-Kahng cluster system without growth restrictions on the kinetic coefficients, using dissipative properties to control the system's behavior.

Contribution

It extends previous results by removing growth conditions on kinetic coefficients and constructs classical solutions under certain conditions.

Findings

Existence of global mild solutions without growth restrictions

Control of infinite sums via dissipative features

Construction of classical solutions for specific coefficients

Abstract

Existence of global mild solutions to the infinite dimensional Redner--ben-Avraham--Kahng cluster system is shown without growth or structure condition on the kinetic coefficients, thereby extending previous results in the literature. The key idea is to exploit the dissipative features of the system to derive a control on the tails of the infinite sums involved in the reaction terms. Classical solutions are also constructed for a suitable class of kinetic coefficients and initial conditions.