Nonlinear stability of critical pulled fronts via resolvent expansions

Abstract: We consider invasion processes mediated by propagating fronts in spatially extended systems, in which a stable rest state invades an unstable rest state. We focus on the case of pulled fronts, for which the speed of propagation is the linear spreading speed, which marks the transition between pointwise decay and pointwise growth for the linearization about the unstable rest state in a co-moving frame. In a general setting of scalar parabolic equations on the real line of arbitrary order, we establish sharp decay rates and temporal asymptotics for perturbations to the front, under conceptual assumptions on the existence and spectral stability of fronts. Some of these results are known for the specific example of the Fisher-KPP equation, and so our work can be viewed as establishing universality of certain aspects of this classical model. Technically, our approach is based on a detailed study of the resolvent operator for the linearization about the critical front, near its essential spectrum.

analysis of PDEsclassical analysis and ODEs

Audience: researchers in the topic

HA-GMT-PDE Seminar

Series comments: Description: A senior graduate student/postdoc series in harmonic analysis, geometric measure theory, and partial differential equations.

Meetings will be weekly, and usually will occur on Monday, with some exceptions. For each talk, the Zoom link is made available in the website too. Contact Bruno Poggi at poggi008@umn.edu if you would like to subscribe to the seminar mailing list.