Geodesic
Uniqueness and stability properties of monostable pulsating fronts
Journal of the European Mathematical Society, Tome 13 (2011) no. 2, pp. 345-390 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/jems/256
Classification : 35-XX, 37-XX, 00-XX
Keywords: Traveling fronts, periodic media, uniqueness, stability, reaction-diffusion equations, monostable reaction 
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     author = {Fran\c{c}ois Hamel and Lionel Roques},
     title = {Uniqueness and stability properties of monostable pulsating fronts},
     journal = {Journal of the European Mathematical Society},
     pages = {345--390},
     year = {2011},
     volume = {13},
     number = {2},
     doi = {10.4171/jems/256},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/256/}
}
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François Hamel; Lionel Roques. Uniqueness and stability properties of monostable pulsating fronts. Journal of the European Mathematical Society, Tome 13 (2011) no. 2, pp. 345-390. doi: 10.4171/jems/256

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