[Fronts Progressifs dans les équations intégro-différentielles]
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.
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.
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@article{CRMATH_2003__337_1_25_0,
author = {Coville, J\'erome and Dupaigne, Louis},
title = {Travelling fronts in integrodifferential equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {25--30},
publisher = {Elsevier},
volume = {337},
number = {1},
year = {2003},
doi = {10.1016/S1631-073X(03)00216-4},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(03)00216-4/}
}
TY - JOUR AU - Coville, Jérome AU - Dupaigne, Louis TI - Travelling fronts in integrodifferential equations JO - Comptes Rendus. Mathématique PY - 2003 SP - 25 EP - 30 VL - 337 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(03)00216-4/ DO - 10.1016/S1631-073X(03)00216-4 LA - en ID - CRMATH_2003__337_1_25_0 ER -
%0 Journal Article %A Coville, Jérome %A Dupaigne, Louis %T Travelling fronts in integrodifferential equations %J Comptes Rendus. Mathématique %D 2003 %P 25-30 %V 337 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(03)00216-4/ %R 10.1016/S1631-073X(03)00216-4 %G en %F CRMATH_2003__337_1_25_0
Coville, Jérome; Dupaigne, Louis. Travelling fronts in integrodifferential equations. Comptes Rendus. Mathématique, Tome 337 (2003) no. 1, pp. 25-30. doi : 10.1016/S1631-073X(03)00216-4. http://archive.numdam.org/articles/10.1016/S1631-073X(03)00216-4/
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