- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:05
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
7
2005
2
The speed of propagation for KPP type problems. I: Periodic framework
Henry
Berestycki
Ecole des hautes études en sciences sociales, PARIS Cedex 13, FRANCE
François
Hamel
Université d'Aix-Marseille, MARSEILLE CEDEX 13, FRANCE
Nikolai
Nadirashvili
University of Chicago, CHICAGO, UNITED STATES
Reaction-diffusion equations, travelling fronts, propagation, periodic media, eigenvalue problems
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 article \cite{bh}. 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.
Partial differential equations
General
173
213
10.4171/JEMS/26
http://www.ems-ph.org/doi/10.4171/JEMS/26