# Asymptotic profiles of solutions to convection-diffusion equations

## TL;DR

This paper investigates the long-term behavior of solutions to convection-diffusion equations, identifying conditions under which solutions resemble Gaussian derivatives, self-similar profiles, or hyperbolic N-waves.

## Contribution

It offers a comprehensive analysis of asymptotic profiles for zero mass solutions, classifying their large-time behavior based on initial data characteristics.

## Key findings

- Solutions asymptotically resemble Gaussian derivatives under certain conditions.
- Self-similar solutions describe the long-term behavior for specific initial data.
- Hyperbolic N-waves emerge as asymptotic profiles in particular regimes.

## Abstract

The large time behavior of zero mass solutions to the Cauchy problem for a convection-diffusion equation. We provide conditions on the size and shape of the initial datum such that the large time asymptotics of solutions is given either by the derivative of the Guass-Weierstrass kernel or by a self-similar solution or by a hyperbolic N-wave