# Asymptotic stability of the critical pulled front in a Lotka-Volterra competition model

## TL;DR

This paper proves the nonlinear asymptotic stability of the critical pulled front in a Lotka-Volterra competition model, showing perturbations decay algebraically at a specific rate using advanced semigroup methods.

## Contribution

It establishes the nonlinear stability of the critical front and links decay rates to spectral properties of the linearized operator.

## Key findings

- Perturbations decay at rate t^{-3/2} in weighted space.
- Stability proof uses pointwise semigroup methods.
- Decay rate linked to Evans function spectral analysis.

## Abstract

We prove that the critical pulled front of Lotka-Volterra competition systems is nonlinearly asymptotically stable. More precisely, we show that perturbations of the critical front decay algebraically with rate $t^{-3/2}$ in a weighted $L^\infty$ space. Our proof relies on pointwise semigroup methods and utilizes in a crucial way that the faster decay rate $t^{-3/2}$ is a consequence of the lack of an embedded zero of the Evans function at the origin for the linearized problem around the critical front.