Large time behaviour for a nonlocal diffusion - convection equation related with the gas dynamics

TL;DR

This paper studies the long-term behavior of solutions to a nonlocal diffusion-convection equation related to gas dynamics, using novel scaling and compactness methods to determine asymptotic properties.

Contribution

It introduces new analytical techniques to analyze the asymptotic behavior of nonlocal diffusion-convection equations in gas dynamics.

Findings

First term in the asymptotic expansion of solutions identified

New compactness argument developed for nonlocal equations

Scaling methods applied to understand long-term dynamics

Abstract

In this paper we consider a model that involves nonlocal diffusion and a classical convective term. Using a scaling argument and a new compactness argument we obtain the first term in the asymptotic behavior of the solutions.