Long-time asymptotics for nonlocal porous medium equation with absorption or convection

TL;DR

This paper investigates the long-term behavior of nonlocal porous medium equations with absorption or convection, demonstrating exponential convergence of solutions under certain conditions using an adapted entropy method.

Contribution

It introduces an adapted entropy method to analyze the exponential convergence of solutions in nonlocal porous medium equations with absorption or convection.

Findings

Exponential convergence of solutions in certain regimes.

Application of entropy method to nonlocal equations.

Insights into asymptotic behavior with dominant nonlocal diffusion.

Abstract

In this paper, the long-time asymptotic behaviours of nonlocal porous medium equations with absorption or convection are studied. In the parameter regimes when the nonlocal diffusion is dominant, the entropy method is adapted in this context to derive the exponential convergence of relative entropy of solutions in similarity variables.