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

Grégory Faye (1) , Matt Holzer (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 George Mason University [Fairfax]

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 ∞ 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.

Mots clés: Lotka-Volterra system; nonlinear stability; pointwise Green's function

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Grégory Faye, Matt Holzer. Asymptotic stability of the critical pulled front in a Lotka-Volterra competition model. Journal of Differential Equations, 2020, 269 (9), ⟨10.1016/j.jde.2020.05.012⟩. ⟨hal-02092829⟩