[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.
Accepté le :
Publié le :
@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://www.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://www.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://www.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://www.numdam.org/articles/10.1016/S1631-073X(03)00216-4/
[1] Travelling waves in a convolution model for phase transition, Arch. Rational Mech. Anal., Volume 138 (1997), pp. 105-136
[2] Stability of travelling fronts in a model for flame propagation. I. Linear analysis, Arch. Rational Mech. Anal., Volume 117 (1992) no. 2, pp. 97-117
[3] Travelling wave solutions to combustion models and their singular limits, SIAM J. Math. Anal., Volume 16 (1985) no. 6, pp. 1207-1242
[4] Travelling fronts in cynlinder, Ann. Inst. H. Poincaré, Volume 9 (1992), pp. 497-572
[5] On the method of moving planes and the slidding method, Bol. Soc. Brasil. Mat., Volume 22 (1991) no. 1, pp. 1-37
[6] Existence, uniqueness and asymptotic stability of travelling fronts in non-local evolution equations, Adv. Differential Equation, Volume 2 (1997), pp. 125-160
[7] J. Coville, Travelling waves in a non-local combustion model, Preprint
[8] J. Coville, L. Dupaigne, Nonlocal population dynamics, Preprint
[9] J. Coville, L. Dupaigne, Front speeds in nonlocal reaction–diffusion equations, Preprint
[10] The approach of solutions of nonlinear diffusion equation to travelling front solutions, Arch. Rational Mech. Anal., Volume 65 (1977), pp. 335-361
[11] The Genetical Theory of Natural Selection, Oxford University Press, Oxford, 1999
[12] Front Propagation: Theory and Applications, C.I.M.E. Lectures, 1995
Cité par Sources :
