Coupled transport equations with freezing

TL;DR

This paper investigates a system of coupled transport equations with a freezing condition, proving existence and uniqueness of solutions, and exploring their properties within a model of colliding balls.

Contribution

It introduces a new coupled transport model with freezing, establishing mathematical well-posedness and analyzing solution behaviors.

Findings

Existence and uniqueness of continuous solutions proven.

Solutions freeze when they become equal.

The model applies to collisions of densely packed balls.

Abstract

We study a system of two coupled transport equations with freezing. The solutions freeze in time when they are equal. We prove existence and uniqueness of continuous solutions if the initial conditions are continuous. We discuss several qualitative and quantitative properties of the solutions. The equations arise in a model for collisions of a large number of tightly spaced balls.