# Precise tail behaviour of self-similar profiles with infinite mass for Smoluchowski's coagulation equation

## TL;DR

This paper analyzes the precise asymptotic tail behavior of self-similar solutions with infinite mass for Smoluchowski's coagulation equation, focusing on fat-tailed profiles with algebraic decay under mild kernel assumptions.

## Contribution

It provides the first detailed asymptotic description of fat-tailed self-similar profiles with infinite mass for a broad class of coagulation kernels.

## Key findings

- Derived exact asymptotics for tail behavior of self-similar profiles.
- Applicable to a wide class of coagulation kernels with mild assumptions.
- Enhanced understanding of infinite-mass solutions in coagulation dynamics.

## Abstract

We consider self-similar profiles to Smoluchowski's coagulation equation for which we derive the precise asymptotic behaviour at infinity. More precisely, we look at so-called fat-tailed profiles which decay algebraically and as a consequence have infinite total mass. The results only require mild assumptions on the coagulation kernel and thus cover a large class of rate kernels.