Fisher-KPP propagation in the presence of a line: further effects

TL;DR

This paper extends a biological invasion model by incorporating transport and reaction on a line, analyzing how these features influence the invasion speed and under what conditions it surpasses the classical Fisher-KPP speed.

Contribution

It introduces new features such as transport and reaction on the line and determines their impact on invasion speed compared to the classical model.

Findings

Transport and reaction terms can enhance propagation speed.

Conditions depend on diffusivity ratios, transport, and reactions.

Asymptotic behaviors are characterized for large parameters.

Abstract

This paper is a continuation of [2] where a new model of biological invasions in the plane directed by a line was introduced. Here we include new features such as transport and reaction terms on the line. Their interaction with the pure diffusivity in the plane is quantified in terms of enhancement of the propagation speed. We establish conditions that determine whether the spreading speed exceeds the standard Fisher KPP invasion speed. These conditions involve the ratio of the diffusivities on the line and in the field, the transport term and the reactions. We derive the asymptotic behaviour for large diffusions or large transports. We also discuss the biological interpretation of these findings.