Truncation of contact defects in reaction-diffusion systems

TL;DR

This paper investigates whether contact defects in reaction-diffusion systems persist when the spatial domain is truncated, demonstrating their existence and uniqueness on sufficiently large intervals for theoretical and numerical analysis.

Contribution

It proves the existence and uniqueness of truncated contact defects in reaction-diffusion systems on large spatial domains.

Findings

Truncated contact defects exist on sufficiently large intervals.

Such defects are unique within these large domains.

The results facilitate better theoretical and numerical understanding.

Abstract

Contact defects are time-periodic patterns in one space dimension that resemble spatially homogeneous oscillations with an embedded defect in their core region. For theoretical and numerical purposes, it is important to understand whether these defects persist when the domain is truncated to large spatial intervals, supplemented by appropriate boundary conditions. The present work shows that truncated contact defects exist and are unique on sufficiently large spatial intervals.