Fractional cross-diffusion in a bounded domain: existence, weak-strong uniqueness, and long-time asymptotics

TL;DR

This paper investigates a fractional cross-diffusion model for multi-species populations in bounded domains, establishing existence, uniqueness, and long-term behavior of solutions using entropy methods.

Contribution

It provides new mathematical results on existence, uniqueness, and asymptotic stability for fractional cross-diffusion systems in bounded domains.

Findings

Existence of solutions proved

Weak-strong uniqueness established

Solutions converge to equilibrium over time

Abstract

We study a fractional cross-diffusion system that describes the evolution of multi-species populations in the regime of large-distance interactions in a bounded domain. We prove existence and weak-strong uniqueness results for the initial-boundary value problem and analyze the convergence of the solutions to equilibrium via relative entropy methods.