# Decay estimates in time for classical and anomalous diffusion

## TL;DR

This paper investigates how solutions to classical and anomalous diffusion equations decay over time within bounded domains, considering fractional and nonlinear operators and their impact on long-term behavior.

## Contribution

It provides new decay estimates for solutions of fractional and nonlinear diffusion equations, highlighting the influence of fractional operators on asymptotic behavior.

## Key findings

- Decay rates for classical diffusion solutions
- Impact of fractional operators on long-time asymptotics
- Decay estimates for nonlinear diffusion equations

## Abstract

We present a series of results focused on the decay in time of solutions of classical and anomalous diffusive equations in a bounded domain. The size of the solution is measured in a Lebesgue space, and the setting comprises time-fractional and space-fractional equations and operators of nonlinear type. We also discuss how fractional operators may affect long-time asymptotics.