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SUMMARY:Montie Avery (University of Minnesota)
DTSTART:20200625T150000Z
DTEND:20200625T155000Z
DTSTAMP:20260423T024839Z
UID:anpdews/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/anpdews/28/"
 >Nonlinear stability of critical pulled fronts via resolvent expansions</a
 >\nby Montie Avery (University of Minnesota) as part of HA-GMT-PDE Seminar
 \n\n\nAbstract\nWe consider invasion processes mediated by propagating fro
 nts in spatially extended systems\, in which a stable rest state invades a
 n unstable rest state. We focus on the case of pulled fronts\, for which t
 he speed of propagation is the linear spreading speed\, which marks the tr
 ansition between pointwise decay and pointwise growth for the linearizatio
 n 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 es
 tablish sharp decay rates and temporal asymptotics for perturbations to th
 e front\, under conceptual assumptions on the existence and spectral stabi
 lity of fronts. Some of these results are known for the specific example o
 f 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 l
 inearization about the critical front\, near its essential spectrum.\n
LOCATION:https://researchseminars.org/talk/anpdews/28/
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