Asymptotic Spreading for General Heterogeneous Fisher-KPP Type Equations

In this monograph, we review the theory and establish new and general results regarding spreading properties for heterogeneous reaction-diffusion equations: The characterizations of these sets involve two new notions of generalized principal eigenvalues for linear parabolic operators in unbounded do...

Ausführliche Beschreibung

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Bibliographische Detailangaben
Hauptverfasser: Berestycki, Henri, Nadin, Grégoire
Format: E-Book Buch
Sprache:Englisch
Veröffentlicht: Providence, Rhode Island American Mathematical Society 2022
Ausgabe:1
Schriftenreihe:Memoirs of the American Mathematical Society
Schlagworte:
Asymptotic theory
Differential equations, Parabolic
Reaction-diffusion equations
linear parabolic operator
slowly oscillating media
Hamilton-Jacobi equations
homogenization
heterogeneous reaction-diffusion equations
unique ergodicity
Reaction-diffusion equations
propagation and spreading properties
principal eigenvalues
almost periodicity
ISBN:9781470454296, 1470454297
ISSN:0065-9266, 1947-6221
Online-Zugang:Volltext
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Inhaltsangabe:
  • Introduction -- A general formula for the expansion sets -- Exact asymptotic spreading speed in different frameworks -- Properties of the generalized principal eigenvalues -- Proof of the spreading property -- The homogeneous, periodic and compactly supported cases -- The almost periodic case -- The uniquely ergodic case -- The radially periodic case -- The space-independent case -- The directionally homogeneous case -- Proof of the spreading property with the alternative definition of the expansion sets and applications -- Further examples and other open problems