@article{AIHPC_1997__14_5_555_0,
author = {Hamel, Fran\c{c}ois},
title = {Reaction-diffusion problems in cylinders with no invariance by translation. {Part} {II} : monotone perturbations},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {555--596},
publisher = {Gauthier-Villars},
volume = {14},
number = {5},
year = {1997},
mrnumber = {1470782},
zbl = {0902.35036},
language = {en},
url = {http://archive.numdam.org/item/AIHPC_1997__14_5_555_0/}
}
TY - JOUR AU - Hamel, François TI - Reaction-diffusion problems in cylinders with no invariance by translation. Part II : monotone perturbations JO - Annales de l'I.H.P. Analyse non linéaire PY - 1997 SP - 555 EP - 596 VL - 14 IS - 5 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPC_1997__14_5_555_0/ LA - en ID - AIHPC_1997__14_5_555_0 ER -
%0 Journal Article %A Hamel, François %T Reaction-diffusion problems in cylinders with no invariance by translation. Part II : monotone perturbations %J Annales de l'I.H.P. Analyse non linéaire %D 1997 %P 555-596 %V 14 %N 5 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPC_1997__14_5_555_0/ %G en %F AIHPC_1997__14_5_555_0
Hamel, François. Reaction-diffusion problems in cylinders with no invariance by translation. Part II : monotone perturbations. Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997) no. 5, pp. 555-596. http://archive.numdam.org/item/AIHPC_1997__14_5_555_0/
[1] and , Properties of solutions of ordinary differential equations in Banach space, Comm. Pure Appl. Math., Vol. 16, 1963, pp. 121-239. | MR | Zbl
[2] and , Multidimensional nonlinear diffusions arising in population genetics, Adv. in Math., Vol. 30, 1978, pp. 33-58. | MR | Zbl
[3] and , Quelques aspects mathématiques de la propagation des flammes prémélangées, Nonlinear p.d.e. and their applications, Collège de France seminar, Vol. 10, Brézis and Lions eds, Pitman Longman, Harbow, UK, 1990. | MR | Zbl
[4] and , A semilinear elliptic equation in a strip arising in a two-dimensional flame propagation model, J. Reine Angew. Math., Vol. 396, 1989, pp. 14-40. | EuDML | MR | Zbl
[5] , and , Multidimensional traveling-wave solutions of a flame propagation model, Arch. Rat. Mech. Anal., Vol. 111, 1990, pp. 33-49. | MR | Zbl
[6] , and , Stability of traveling fronts in a curved flame model, Part I, Linear Analysis, Arch. Rat. Mech. Anal., Vol. 117, 1992, pp. 97-117. | MR | Zbl
[7] and , Travelling fronts in cylinders, Ann. Inst. H. Poincaré, Analyse Non Linéaire, Vol. 9, 5, 1992, pp. 497-572. | EuDML | Numdam | MR | Zbl
[8] and , On the method of moving planes and the sliding method, Bol. da Soc. Braseleira de Matematica, Vol. 22, 1991, pp. 1-37. | MR | Zbl
[9] and , The approach of solutions of non-linear diffusion equations to traveling front solutions, Arch. Rat. Mech. Anal., Vol. 65, 1977, pp. 335-361. | MR | Zbl
[10] , Reaction-diffusion problems in cylinders with no invariance by translation, part I: Small perturbations, Ann. Inst. H. Poincaré, Analyse Non Linéaire, Vol. 14, 1997, pp. 457-498. | Numdam | MR | Zbl
[11] , Formules min-max pour les vitesses d'ondes progressives multidimensionnelles, preprint Labo. Ana. Num., n° 96032, Univ. Paris VI, France, 1996.
[12] , Stabilization of solution of the Cauchy problem for equations encountred in combustion theory, Mat. Sbornik., Vol. 59, 1962, pp. 245-288. | MR | Zbl
[13] , and , Etude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, Bulletin Université d'Etat à Moscow (Bjul. Moskowskogo Gos. Univ.), Série intemationale, section A.1, 1937, pp. 1-26. | Zbl
[14] , Fluid Dynamic Aspects of Combustion Theory, course of IAC. Mauro Picone, Rome, 1989.
[15] , Asymptotic expansions of solutions of ordinary differential equations in Hilbert space, Arch. Rat. Mech. Anal., Vol. 24, 1967, pp. 193-218. | MR | Zbl
[16] , Instabilities, pattern formation and turbulence in flames, Ann. Rev. Fluid Mech., Vol. 15, 1983, pp. 179-199. | Zbl
[17] , On the uniqueness of multidimensional travelling fronts of some semilinear equations, J. Math. Anal. Appl., Vol. 177, 1993, pp. 481-490. | MR | Zbl
[18] , The asymptotic behavior of the solutions of some semilinear elliptic equations in cylindrical domains, J. Diff. Eq., Vol. 102, 1993, pp. 119-152. | MR | Zbl
[19] and , Existence and Stability of Stationary Solutions for a Class of Semilinear Parabolic Systems, Comm. in Part. Diff. Eq., Vol. 18, 1993, pp. 2051-2069. | MR | Zbl
[20] , Combustion Theory, Addison-Wesley, reading MA, 1983.
[21] , Existence and Uniqueness of Travelling Waves in a Reaction-Diffusion Equation with Combustion Nonlinearity, Idiana Univ. Math. J., Vol. 40, No 3, 1991. | MR | Zbl
[22] , Existence of planar flame fronts in convective-diffusive periodic media, Arch. Rat. Mech. Analysis, Vol. 121, 1992, pp. 205-233. | MR | Zbl
[23] , Existence and stability of travelling waves in periodic media governed by a bistable nonlinearity, J. Dyn. Diff. Eq., Vol. 3, 1991, pp. 541-573. | MR | Zbl
[24] , Existence and non existence of travelling waves and reaction-diffusion front propagation in periodic media, J. Statist. Phys., Vol. 73, 1993, pp. 893-926. | MR | Zbl
[25] and , A theory of thermal propagation of flame, Acta physiochimica URSS, Vol. 9, 1938. English translation in Dynamics of curved fronts, R. Pelcé ed., Perspectives in Physics Series, Academic Press, New York, 1988, pp. 131-140.
