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.
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.
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@article{CRMATH_2004__339_10_699_0,
author = {Hamel, Fran\c{c}ois and Monneau, R\'egis and Roquejoffre, Jean-Michel},
title = {Existence et propri\'et\'es qualitatives de fronts coniques bistables en dimension 2 d'espace},
journal = {Comptes Rendus. Math\'ematique},
pages = {699--704},
publisher = {Elsevier},
volume = {339},
number = {10},
year = {2004},
doi = {10.1016/j.crma.2004.09.020},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.09.020/}
}
TY - JOUR AU - Hamel, François AU - Monneau, Régis AU - Roquejoffre, Jean-Michel TI - Existence et propriétés qualitatives de fronts coniques bistables en dimension 2 d'espace JO - Comptes Rendus. Mathématique PY - 2004 SP - 699 EP - 704 VL - 339 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.09.020/ DO - 10.1016/j.crma.2004.09.020 LA - fr ID - CRMATH_2004__339_10_699_0 ER -
%0 Journal Article %A Hamel, François %A Monneau, Régis %A Roquejoffre, Jean-Michel %T Existence et propriétés qualitatives de fronts coniques bistables en dimension 2 d'espace %J Comptes Rendus. Mathématique %D 2004 %P 699-704 %V 339 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.09.020/ %R 10.1016/j.crma.2004.09.020 %G fr %F CRMATH_2004__339_10_699_0
Hamel, François; Monneau, Régis; Roquejoffre, Jean-Michel. Existence et propriétés qualitatives de fronts coniques bistables en dimension 2 d'espace. Comptes Rendus. Mathématique, Tome 339 (2004) no. 10, pp. 699-704. doi : 10.1016/j.crma.2004.09.020. http://www.numdam.org/articles/10.1016/j.crma.2004.09.020/
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