The logarithmic delay of KPP fronts in a periodic medium

François Hamel; James Nolen; Jean-Michel Roquejoffre; Lenya Ryzhik

Journal of the European Mathematical Society (2016)

  • Volume: 018, Issue: 3, page 465-505
  • ISSN: 1435-9855

Abstract

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We extend, to parabolic equations of the KPP type in periodic media, a result of Bramson which asserts that, in the case of a spatially homogeneous reaction rate, the time lag between the position of an initially compactly supported solution and that of a traveling wave grows logarithmically in time.

How to cite

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Hamel, François, et al. "The logarithmic delay of KPP fronts in a periodic medium." Journal of the European Mathematical Society 018.3 (2016): 465-505. <http://eudml.org/doc/277563>.

@article{Hamel2016,
abstract = {We extend, to parabolic equations of the KPP type in periodic media, a result of Bramson which asserts that, in the case of a spatially homogeneous reaction rate, the time lag between the position of an initially compactly supported solution and that of a traveling wave grows logarithmically in time.},
author = {Hamel, François, Nolen, James, Roquejoffre, Jean-Michel, Ryzhik, Lenya},
journal = {Journal of the European Mathematical Society},
keywords = {reaction-diffusion equations; periodic media; pulsating traveling fronts; Cauchy problem; asymptotic behavior; logarithmic shift; propagation; periodic medium; reaction-diffusion equation; pulsating front; logarithmic time shift},
language = {eng},
number = {3},
pages = {465-505},
publisher = {European Mathematical Society Publishing House},
title = {The logarithmic delay of KPP fronts in a periodic medium},
url = {http://eudml.org/doc/277563},
volume = {018},
year = {2016},
}

TY - JOUR
AU - Hamel, François
AU - Nolen, James
AU - Roquejoffre, Jean-Michel
AU - Ryzhik, Lenya
TI - The logarithmic delay of KPP fronts in a periodic medium
JO - Journal of the European Mathematical Society
PY - 2016
PB - European Mathematical Society Publishing House
VL - 018
IS - 3
SP - 465
EP - 505
AB - We extend, to parabolic equations of the KPP type in periodic media, a result of Bramson which asserts that, in the case of a spatially homogeneous reaction rate, the time lag between the position of an initially compactly supported solution and that of a traveling wave grows logarithmically in time.
LA - eng
KW - reaction-diffusion equations; periodic media; pulsating traveling fronts; Cauchy problem; asymptotic behavior; logarithmic shift; propagation; periodic medium; reaction-diffusion equation; pulsating front; logarithmic time shift
UR - http://eudml.org/doc/277563
ER -

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