Journal
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
Volume 13, Issue 2, Pages 345-390Publisher
EUROPEAN MATHEMATICAL SOC-EMS
DOI: 10.4171/JEMS/256
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- Alexander von Humboldt Foundation
- French Agence Nationale de la Recherche
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We prove the uniqueness, up to shifts, of pulsating traveling fronts for reaction-diffusion equations in periodic media with Kolmogorov-Petrovskii-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.
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