Mass-Conserving Self-Similar Solutions to Collision-Induced Breakage Equations

TL;DR

This paper proves the existence of mass-conserving self-similar solutions for collision-induced breakage equations using a dynamical approach, providing bounds for the scaling profile.

Contribution

It introduces a novel dynamical and compactness method to establish mass-conserving solutions for specific collision kernels and breakage functions.

Findings

Existence of mass-conserving self-similar solutions proved.

Bounds for the scaling profile determined.

Method applicable to specific collision kernels.

Abstract

Existence of mass-conserving self-similar solutions to collision-induced breakage equation is shown for a specific class of homogeneous collision kernels and breakage functions. The proof mainly relies on a dynamical approach and compactness method to constructing mass-conserving stationary solutions for an evolution problem, which induces mass-conserving self-similar solutions to collision-induced breakage equation. Furthermore, we also determine lower and upper bound of the scaling profile.