Self-similar solutions with fat tails for a coagulation equation with nonlocal drift

TL;DR

This paper studies self-similar solutions to a coagulation equation with nonlocal drift, revealing both exponential and algebraic decay profiles, expanding understanding of solution behaviors.

Contribution

It establishes the existence of self-similar solutions with algebraic decay, complementing known exponential solutions, for a coagulation equation with nonlocal drift.

Findings

Existence of self-similar solutions with algebraic decay.

Explicit exponentially decaying solutions identified.

Broadened understanding of solution profiles in coagulation equations.

Abstract

We investigate the existence of self-similar solutions for a coagulation equation with nonlocal drift. In addition to explicitly given exponentially decaying solutions we establish the existence of self-similar profiles with algebraic decay.