# The speed of propagation for KPP type problems. I: Periodic framework

Henry Berestycki; François Hamel; Nikolai Nadirashvili

Journal of the European Mathematical Society (2005)

- Volume: 007, Issue: 2, page 173-213
- ISSN: 1435-9855

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topBerestycki, Henry, Hamel, François, and Nadirashvili, Nikolai. "The speed of propagation for KPP type problems. I: Periodic framework." Journal of the European Mathematical Society 007.2 (2005): 173-213. <http://eudml.org/doc/277219>.

@article{Berestycki2005,

abstract = {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 [7]. 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.},

author = {Berestycki, Henry, Hamel, François, Nadirashvili, Nikolai},

journal = {Journal of the European Mathematical Society},

keywords = {reaction-diffusion equations; travelling fronts; propagation; periodic media; eigenvalue problems},

language = {eng},

number = {2},

pages = {173-213},

publisher = {European Mathematical Society Publishing House},

title = {The speed of propagation for KPP type problems. I: Periodic framework},

url = {http://eudml.org/doc/277219},

volume = {007},

year = {2005},

}

TY - JOUR

AU - Berestycki, Henry

AU - Hamel, François

AU - Nadirashvili, Nikolai

TI - The speed of propagation for KPP type problems. I: Periodic framework

JO - Journal of the European Mathematical Society

PY - 2005

PB - European Mathematical Society Publishing House

VL - 007

IS - 2

SP - 173

EP - 213

AB - 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 [7]. 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.

LA - eng

KW - reaction-diffusion equations; travelling fronts; propagation; periodic media; eigenvalue problems

UR - http://eudml.org/doc/277219

ER -

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