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Comptes Rendus Mathématique
Volume 339, n° 10
pages 699-704 (novembre 2004)
Doi : 10.1016/j.crma.2004.09.020
Received : 5 June 2004 ;  accepted : 14 June 2004
Existence et propriétés qualitatives de fronts coniques bistables en dimension 2 d'espace
Existence and qualitative properties of bistable conical fronts in two space dimensions.
 

François Hamel a , Régis Monneau b , Jean-Michel Roquejoffre c
a UMR CNRS 6632 (LATP), université Aix-Marseille III, avenue Escadrille-Normandie-Niemen, 13397 Marseille cedex 20, France 
b CERMICS-ENPC, 6-8, avenue B. Pascal, cité Descartes, 77455 Marne-La-Vallée cedex 2, France 
c UMR CNRS 5640 (MIP) et IUF, université Paul Sabatier, 118, route de Narbone, 31062 Toulouse cedex 4, France 

Résumé

On donne dans cette note des résultats d'existence d'ondes progressives à lignes de niveaux coniques pour une équation de réaction-diffusion à non-linéarité bistable. Les solutions trouvées ici ont une vitesse plus grande que l'onde monodimensionnelle. Leurs lignes de niveaux sont asymptotes à des droites, dont l'angle avec la verticale se calcule en fonction de la vitesse des ondes. Des propriétés qualitatives : monotonie, symétrie, convergence exponentielle des pentes des lignes de niveau, sont discutées. Pour citer cet article : F. Hamel et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).

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Abstract

Conical-shaped travelling wave solutions of a bistable reaction-diffusion equations posed in the plane are shown to exist. The velocity of the wave solutions is strictly larger than the planar wave velocity, and their level sets are asymptotic to lines whose angle is computed in terms of their velocity. Qualitative properties, such as monotonicity, symmetry, and exponential convergence of the slopes of the level lines, are given. To cite this article: F. Hamel et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).

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