Travelling Fronts and Entire Solutions¶of the Fisher-KPP Equation in ℝN View Full Text


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Article Info

DATE

2001-04

AUTHORS

François Hamel, Nikolaï Nadirashvili

ABSTRACT

This paper is devoted to time-global solutions of the Fisher-KPP equation in ℝN:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} where f is a C2 concave function on [0,1] such that f(0)=f(1)=0 and f>0 on (0,1). It is well known that this equation admits a finite-dimensional manifold of planar travelling-fronts solutions. By considering the mixing of any density of travelling fronts, we prove the existence of an infinite-dimensional manifold of solutions. In particular, there are infinite-dimensional manifolds of (nonplanar) travelling fronts and radial solutions. Furthermore, up to an additional assumption, a given solution u can be represented in terms of such a mixing of travelling fronts. More... »

PAGES

91-163

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/pl00004238

DOI

http://dx.doi.org/10.1007/pl00004238

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1043031733


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