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Comptes Rendus Mathématique
Volume 337, n° 1
pages 25-30 (juillet 2003)
Doi : 10.1016/S1631-073X(03)00216-4
Received : 2 April 2003 ;  accepted : 2 April 2003
Travelling fronts in integrodifferential equations

Jérome  Coville,  Louis  Dupaigne
Laboratoire Jacques-Louis Lions, Université Paris VI, 175, rue du Chevaleret, 75013 Paris, France 

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We provide results of the existence, uniqueness and asymptotic behavior of travelling-wave solutions for convolution equations involving different kinds of nonlinearities (bistable, ignition and monostable). We recover for these equations most of the known results about the standard equation  . Some min-max formulas are also given. To cite this article: J. Coville, L. Dupaigne, C. R. Acad. Sci. Paris, Ser. I 337 (2003).

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On présente plusieurs résultats concernant les solutions de type front progressif dans des équations de réaction-diffusion intégro-différentielles 1D faisant intervenir divers types de non-linéarités (bistable, ignition, monostable). On étend à ces équations des résultats connus dans le cadre d'une équation de réaction-diffusion usuelle : l'existence de telles solutions est notemment démontrée pour les trois types de nonlinéarités citées. L'unicité et quelques formules caractérisant la vitesse de ces fronts sont aussi établies dans certains cas. Pour citer cet article : J. Coville, L. Dupaigne, C. R. Acad. Sci. Paris, Ser. I 337 (2003).




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