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...

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Bibliographic Details
Main Authors:	Berestycki, Henri, Nadin, Grégoire
Format:	eBook Book
Language:	English
Published:	Providence, Rhode Island American Mathematical Society 2022
Edition:	1
Series:	Memoirs of the American Mathematical Society
Subjects:	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 Access:	Get full text
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Table of Contents:

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