The speed of propagation for KPP type problems. I: Periodic framework
type: Item
instance of: scholarly article
title: The speed of propagation for KPP type problems. I: Periodic framework
zbMATH Open document ID: 1142.35464
DOI: 10.4171/JEMS/26
author: Henri Berestycki
author: François Hamel
author: Nikolai Nadirashvili
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2005-05-03T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_abstract.php
review text: Summary: This paper is devoted to some nonlinear propagation phenomena in periodic and more general domains, for reaction-diffusion equations with Kolmogorov-Petrovsky-Piskunov (KPP) type nonlinearities. The case of periodic domains with periodic underlying excitable media is a follow-up of the first two authors' article [Commun. Pure Appl. Math. 55, No. 8, 949--1032 (2002; Zbl 1024.37054)]. It is proved that the minimal speed of pulsating fronts is given by a variational formula involving linear eigenvalue problems. Some consequences concerning the influence of the geometry of the domain, of the reaction, advection and diffusion coefficients are given. The last section deals with the notion of asymptotic spreading speed. The main properties of the spreading speed are given. Some of them are based on some new Liouville type results for nonlinear elliptic equations in unbounded domains.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 2164660
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2164660