- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:06
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
13
2011
2
Uniqueness and stability properties of monostable pulsating fronts
François
Hamel
Université d'Aix-Marseille, MARSEILLE CEDEX 13, FRANCE
Lionel
Roques
UR546 Biostatistique et Processus Spatiaux, AVIGNON, FRANCE
Traveling fronts, periodic media, uniqueness, stability, reaction-diffusion equations, monostable reaction
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.
Partial differential equations
Dynamical systems and ergodic theory
General
345
390
10.4171/JEMS/256
http://www.ems-ph.org/doi/10.4171/JEMS/256