Asymptotics for nonlocal evolution problems by scaling arguments

TL;DR

This paper investigates the long-term behavior of solutions to a nonlocal evolution problem using a novel scaling method that distinguishes between smooth and rough solution components.

Contribution

It introduces a new scaling approach to derive the leading asymptotic term for nonlocal evolution equations, handling smooth and rough parts separately.

Findings

First asymptotic term derived for nonlocal evolution solutions

Method distinguishes smooth and rough solution components

Provides a new analytical tool for nonlocal problems

Abstract

In this paper we consider a nonlocal evolution problem and obtain by a scaling method the first term in the asymptotic behavior of the solutions. The method employed treats in different way the smooth and the rough part of the solution.