A kinetic equation for repulsive coalescing random jumps in continuum

TL;DR

This paper introduces a continuum model for particles that hop and coalesce, deriving a kinetic equation through scaling and proving its well-posedness, advancing understanding of such stochastic systems.

Contribution

It presents a new kinetic equation for coalescing particles in continuum and establishes existence and uniqueness of its solutions.

Findings

Derived a hierarchy of evolution equations for the microscopic dynamics

Performed a Vlasov-type scaling to connect micro- and mesoscopic models

Proved existence and uniqueness of solutions to the kinetic equation

Abstract

A continuum individual-based model of hopping and coalescing particles is introduced and studied. Its microscopic dynamics are described by a hierarchy of evolution equations obtained in the paper. Then the passage from the micro- to mesoscopic dynamics is performed by means of a Vlasov-type scaling. The existence and uniqueness of the solutions of the corresponding kinetic equation are proved.