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Article Dans Une Revue Journal of the European Mathematical Society Année : 2011

Uniqueness and stability properties of monostable pulsating fronts

François Hamel
Lionel Roques

Résumé

In this paper, we prove the uniqueness, up to shifts, of pulsating traveling fronts for reaction-diffusion equations in periodic media with Kolmogorov-Petrovsky-Piskunov type nonlinearities. These results provide in particular a complete classification of all KPP pulsating fronts. Furthermore, in the more general case of monostable nonlineari-ties, we also derive several global stability properties and convergence to the pulsating fronts for the 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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hal-01257395 , version 1 (16-01-2016)

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François Hamel, Lionel Roques. Uniqueness and stability properties of monostable pulsating fronts. Journal of the European Mathematical Society, 2011, 13, pp.345-390. ⟨10.4171/JEMS/256⟩. ⟨hal-01257395⟩
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