# Influence of the geometry on a field-road model : the case of a conical field

## TL;DR

This paper investigates how the shape of a conical field affects the spread of a reaction-diffusion process coupled with a road, finding that the cone's angle does not influence the spreading speed.

## Contribution

It extends field-road models to conical geometries, showing the spreading speed remains unaffected by the cone's angle, unlike in straight-line cases.

## Key findings

- Spreading speed is independent of the cone's angle.
- The model generalizes previous straight-line results.
- The cone geometry does not alter propagation speed.

## Abstract

Field-road models are reaction-diffusion systems which have been recently introduced to account for the effect of a road on propagation phenomena arising in epidemiology and ecology. Such systems consist in coupling a classical Fisher-KPP equation to a line with fast diffusion accounting for a road. A series of works investigate the spreading properties of such systems when the road is a straight line and the field a half-plane. Here, we take interest in the case where the field is a cone. Our main result is that the spreading speed is not influenced by the angle of the cone.