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Spectral stability of the critical front in the extended Fisher-KPP equation

Avery, Montie ; Garénaux, Louis ORCID iD icon 1
1 Institut für Analysis (IANA), Karlsruher Institut für Technologie (KIT)


We revisit the existence and stability of the critical front in the extended Fisher-KPP equation, refining earlier results of Rottschäfer and Wayne [28] which establish stability of fronts without identifying a precise decay rate. We verify that the front is marginally spectrally stable: while the essential spectrum touches the imaginary axis at the origin, there are no unstable eigenvalues and no eigenvalue (or resonance) embedded in the essential spectrum at the origin. Together with the recent work of Avery and Scheel [3], this implies nonlinear stability of the critical front with sharp $t^{−3/2}$ decay rate, as previously obtained in the classical Fisher-KPP equation. The main challenges are to regularize the singular perturbation in the extended Fisher-KPP equation and to track eigenvalues near the essential spectrum, and we overcome these difficulties with functional analytic methods.

Volltext §
DOI: 10.5445/IR/1000156983
Veröffentlicht am 16.03.2023
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2020
Sprache Englisch
Identifikator KITopen-ID: 1000156983
Umfang 21 S.
Vorab online veröffentlicht am 03.09.2020
Nachgewiesen in arXiv
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