Uniqueness and stability properties of monostable pulsating fronts

Hamel, François, and Roques, Lionel. "Uniqueness and stability properties of monostable pulsating fronts." Journal of the European Mathematical Society 013.2 (2011): 345-390. <http://eudml.org/doc/277376>.

@article{Hamel2011,
abstract = {We prove the uniqueness, up to shifts, of pulsating traveling fronts for reaction-diffusion equations in periodic media with Kolmogorov–Petrovskiĭ–Piskunov type nonlinearities. These results provide in particular a complete classification of all KPP pulsating fronts. Furthermore, in the more general case of monostable nonlinearities, we also derive several global stability properties and convergence to pulsating fronts for solutions of the Cauchy problem with front-like initial data. In particular, we prove the stability of KPP pulsating fronts with minimal speed, which is a new result even in the case when the medium is invariant in the direction of propagation.},
author = {Hamel, François, Roques, Lionel},
journal = {Journal of the European Mathematical Society},
keywords = {traveling fronts; periodic media; uniqueness; stability; reaction-diffusion equations; monostable reaction; Kolmogorov-Petrovskii-Piskunov type nonlinearities; Kolmogorov-Petrovskii-Piskunov type nonlinearities; periodic media},
language = {eng},
number = {2},
pages = {345-390},
publisher = {European Mathematical Society Publishing House},
title = {Uniqueness and stability properties of monostable pulsating fronts},
url = {http://eudml.org/doc/277376},
volume = {013},
year = {2011},
}

TY - JOUR
AU - Hamel, François
AU - Roques, Lionel
TI - Uniqueness and stability properties of monostable pulsating fronts
JO - Journal of the European Mathematical Society
PY - 2011
PB - European Mathematical Society Publishing House
VL - 013
IS - 2
SP - 345
EP - 390
AB - We prove the uniqueness, up to shifts, of pulsating traveling fronts for reaction-diffusion equations in periodic media with Kolmogorov–Petrovskiĭ–Piskunov type nonlinearities. These results provide in particular a complete classification of all KPP pulsating fronts. Furthermore, in the more general case of monostable nonlinearities, we also derive several global stability properties and convergence to pulsating fronts for solutions of the Cauchy problem with front-like initial data. In particular, we prove the stability of KPP pulsating fronts with minimal speed, which is a new result even in the case when the medium is invariant in the direction of propagation.
LA - eng
KW - traveling fronts; periodic media; uniqueness; stability; reaction-diffusion equations; monostable reaction; Kolmogorov-Petrovskii-Piskunov type nonlinearities; Kolmogorov-Petrovskii-Piskunov type nonlinearities; periodic media
UR - http://eudml.org/doc/277376
ER -