Stopping a reaction-diffusion front

TL;DR

This paper investigates how reaction-diffusion fronts interact with defects, revealing that bistable fronts can be pinned while monostable fronts cannot, with implications for biological modeling.

Contribution

It provides a comparative analysis of bistable and monostable reaction-diffusion fronts interacting with defects, including a pinning criterion and dynamic behavior insights.

Findings

Bistable fronts can be pinned by defects.

Monostable fronts cannot be pinned and generate secondary pulses.

The study offers a criterion for pinning and analyzes front dynamics.

Abstract

We revisit the problem of pinning a reaction-diffusion front by a defect, in particular by a reaction-free region. Using collective variables for the front and numerical simulations, we compare the behaviors of a bistable and monostable front. A bistable front can be pinned as confirmed by a pinning criterion, the analysis of the time independant problem and simulations. Conversely, a monostable front can never be pinned, it gives rise to a secondary pulse past the defect and we calculate the time this pulse takes to appear. These radically different behaviors of bistable and monostable fronts raise issues for modelers in particular areas of biology, as for example, the study of tumor growth in the presence of different tissues.