Dynamics and spreading speeds of a nonlocal diffusion model with advection and free boundaries

TL;DR

This paper analyzes a nonlocal diffusion model with advection and free boundaries, establishing conditions for spreading or vanishing, and explicitly describing the spreading speeds influenced by nonlocal diffusion and advection.

Contribution

It introduces a novel analysis of a nonlocal diffusion-advection model with free boundaries, providing explicit spreading speed descriptions and conditions for long-term behaviors.

Findings

Established existence, uniqueness, and regularity of solutions.

Derived conditions for spreading or vanishing.

Explicitly described finite spreading speeds influenced by advection.

Abstract

In this paper, we investigate a Fisher-KPP nonlocal diffusion model incorporating the effect of advection and free boundaries, aiming to explore the propagation dynamics of the nonlocal diffusion-advection model. Considering the effects of the advection, the existence, uniqueness, and regularity of the global solution are obtained. We introduce the principal eigenvalue of the nonlocal operator with the advection term and discuss the asymptotic properties influencing the long-time behaviors of the solution for this model. Moreover, we give several sufficient conditions determining the occurrences of spreading or vanishing and obtain the spreading-vanishing dichotomy. Most of all, applying the semi-wave solution and constructing the upper and the lower solution, we give an explicit description of the finite asymptotic spreading speeds for the double free boundaries on the effects of the nonlocal diffusion and advection compared with the corresponding problem without an advection term.