Self-Similarity for Ballistic Aggregation Equation

TL;DR

This paper studies the ballistic aggregation equation, proving the existence and convergence of self-similar solutions for constant rates, and analyzing decay and new solutions for variable rates.

Contribution

It establishes the existence and convergence of self-similar solutions for the ballistic aggregation equation with constant rates and explores solutions for variable rates.

Findings

Existence of self-similar solutions for constant aggregation rates.

Convergence of generic solutions to self-similarity over time.

Decay estimates and new classes of solutions for variable rates.

Abstract

We consider ballistic aggregation equation for gases in which each particle is iden- ti?ed either by its mass and impulsion or by its sole impulsion. For the constant aggregation rate we prove existence of self-similar solutions as well as convergence to the self-similarity for generic solutions. For some classes of mass and/or impulsion dependent rates we are also able to estimate the large time decay of some moments of generic solutions or to build some new classes of self-similar solutions.