Stability of travelling waves in a model for conical flames in two space dimensions
François Hamel; Régis Monneau; Jean-Michel Roquejoffre
Annales scientifiques de l'École Normale Supérieure (2004)
- Volume: 37, Issue: 3, page 469-506
- ISSN: 0012-9593
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topHamel, François, Monneau, Régis, and Roquejoffre, Jean-Michel. "Stability of travelling waves in a model for conical flames in two space dimensions." Annales scientifiques de l'École Normale Supérieure 37.3 (2004): 469-506. <http://eudml.org/doc/82637>.
@article{Hamel2004,
author = {Hamel, François, Monneau, Régis, Roquejoffre, Jean-Michel},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {ignition temperature; Bunsen burner flames; subsolution; supersolutions; conical shaped travelling wave},
language = {eng},
number = {3},
pages = {469-506},
publisher = {Elsevier},
title = {Stability of travelling waves in a model for conical flames in two space dimensions},
url = {http://eudml.org/doc/82637},
volume = {37},
year = {2004},
}
TY - JOUR
AU - Hamel, François
AU - Monneau, Régis
AU - Roquejoffre, Jean-Michel
TI - Stability of travelling waves in a model for conical flames in two space dimensions
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2004
PB - Elsevier
VL - 37
IS - 3
SP - 469
EP - 506
LA - eng
KW - ignition temperature; Bunsen burner flames; subsolution; supersolutions; conical shaped travelling wave
UR - http://eudml.org/doc/82637
ER -
References
top- [1] Agmon S, Nirenberg L, Properties of solutions of ordinary differential equations in Banach space, Comm. Pure Appl. Math.16 (1963) 121-239. Zbl0117.10001MR155203
- [2] Aronson D.G, Weinberger H.F, Nonlinear diffusion in population genetics, combustion and nerve propagation, in: Part. Diff. Eq. and Related Topics, Lecture Notes in Math., vol. 446, Springer, New York, 1975, pp. 5-49. Zbl0325.35050MR427837
- [3] Berestycki H, Hamel F, Front propagation in periodic excitable media, Comm. Pure Appl. Math.55 (2002) 949-1032. Zbl1024.37054MR1900178
- [4] Berestycki H, Larrouturou B, Lions P.-L, Multidimensional travelling-wave solutions of a flame propagation model, Arch. Rat. Mech. Anal.111 (1990) 33-49. Zbl0711.35066MR1051478
- [5] Berestycki H, Larrouturou B, Roquejoffre J.-M, Stability of travelling fronts in a curved flame model, Part I, Linear analysis, Arch. Rat. Mech. Anal.117 (1992) 97-117. Zbl0763.76033MR1145107
- [6] Berestycki H, Nicolaenko B, Scheurer B, Traveling waves solutions to combustion models and their singular limits, SIAM J. Math. Anal.16 (6) (1985) 1207-1242. Zbl0596.76096MR807905
- [7] Berestycki H, Nirenberg L, On the method of moving planes and the sliding method, Bol. Soc. Bras. Mat.22 (1991) 1-37. Zbl0784.35025MR1159383
- [8] Berestycki H, Nirenberg L, Travelling fronts in cylinders, Ann. Inst. H. Poincaré, Anal. Non Lin.9 (1992) 497-572. Zbl0799.35073MR1191008
- [9] Bonnet A, Hamel F, Existence of non-planar solutions of a simple model of premixed Bunsen flames, SIAM J. Math. Anal.31 (1999) 80-118. Zbl0942.35072MR1742304
- [10] Bramson M, Convergence of Solutions of the Kolmogorov Equation to Travelling Waves, in: Mem. Amer. Math. Soc., vol. 44, 1983. Zbl0517.60083MR705746
- [11] Brazhnik P.K, Tyson J.J, On traveling wave solutions of Fisher's equation in two spatial dimensions, SIAM J. Appl. Math.60 (2000) 371-391. Zbl0957.35065MR1740251
- [12] Buckmaster J.D, Ludford G.S.S, Lectures on Mathematical Combustion, in: CBMS-NSF Conf. Series in Applied Math., vol. 43, SIAM, 1983. Zbl0574.76001MR765073
- [13] Caffarelli L.A, Cabré X, Fully Nonlinear Elliptic Equations, in: Colloquium Publications, Amer. Math. Soc., vol. 43, 1995. Zbl0834.35002MR1351007
- [14] Crandall M.G, Ishii H, Lions P.-L, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.)27 (1992) 1-67. Zbl0755.35015MR1118699
- [15] Collet P, Eckmann J.-P, Space-time behaviour in problems of hydrodynamic type: a case study, Nonlinearity5 (6) (1992) 1265-1302. Zbl0757.35059MR1192518
- [16] Fife P.C, Dynamics of internal layers and diffusive interfaces, in: Cbms-Nsf Regional Conference, Series in Applied Mathematics, vol. 53, 1988. Zbl0684.35001MR981594
- [17] Fife P.C, McLeod J.B, The approach of solutions of non-linear diffusion equations to travelling front solutions, Arch. Rat. Mech. Anal.65 (1977) 335-361. Zbl0361.35035MR442480
- [18] Gilbarg D, Trudinger N.S, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1997. Zbl0562.35001
- [19] Hamel F, Monneau R, Solutions of semilinear elliptic equations in RN with conical-shaped level sets, Comm. Partial Differential Equations25 (2000) 769-819. Zbl0952.35041MR1759793
- [20] Hamel F, Monneau R, Existence and uniqueness for a free boundary problem arising in combustion theory, Interfaces Free Boundaries4 (2002) 167-210. Zbl1078.80004MR1950528
- [21] Hamel F, Nadirashvili N, Travelling waves and entire solutions of the Fisher-KPP equation in RN, Arch. Ration. Mech. Anal.157 (2001) 91-163. Zbl0987.35072MR1830037
- [22] Henry D, Geometric Theory of Semilinear Parabolic Equations, in: Lecture Notes in Math., Springer Verlag, New York, 1981. Zbl0456.35001MR610244
- [23] Ishii H, On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDE's, Comm. Pure Appl. Math.42 (1989) 15-45. Zbl0645.35025MR973743
- [24] Joulin G, Dynamique des fronts de flammes, in: Modélisation de la combustion, Images des Mathématiques, CNRS, 1996.
- [25] Kanel' Ya.I, Certain problems of burning-theory equations, Sov. Math. Dokl.2 (1961) 48-51. Zbl0138.35103MR117429
- [26] Kanel' Ya.I, Stabilization of solution of the Cauchy problem for equations encountered in combustion theory, Mat. Sbornik59 (1962) 245-288. MR157130
- [27] Levermore C.D, Xin J.X, Multidimensional stability of travelling waves in a bistable reaction-diffusion equation, II, Comm. Partial Differential Equations17 (1992) 1901-1924. Zbl0789.35020MR1194744
- [28] Lewis B, Von Elbe G, Combustion, Flames and Explosions of Gases, Academic Press, New York, 1961.
- [29] Mallordy J.-F, Roquejoffre J.-M, A parabolic equation of the KPP type in higher dimensions, SIAM J. Math. Anal.26 (1995) 1-20. Zbl0813.35041MR1311879
- [30] Matkowsky B.J, Olagunju D.O, Pulsations in a burner-stabilized premixed plane flame, SIAM J. Appl. Math.40 (1981) 551-562. Zbl0484.76094MR614749
- [31] Michelson D, Stability of the Bunsen flame profiles in the Kuramoto–Sivashinsky equation, SIAM J. Math. Anal.27 (1996) 765-781. Zbl0851.34020MR1382832
- [32] Ninomiya H., Taniguchi M., Stability of traveling curved fronts in a curvature flow with driving force, Meth. Appl. Anal., submitted for publication. Zbl1007.35004MR1904754
- [33] Roquejoffre J.-M, Stability of travelling fronts in a curved flame model, Part II: Non-linear orbital stability, Arch. Rat. Mech. Anal.117 (1992) 119-153. Zbl0763.76034MR1145108
- [34] Roquejoffre J.-M, Convergence to travelling waves for solutions of a class of semilinear parabolic equation, J. Differential Equations108 (1994) 262-295. Zbl0806.35093MR1270581
- [35] Roquejoffre J.-M, Eventual monotonicity and convergence to travelling fronts for the solutions of parabolic equations in cylinders, Ann. Inst. H. Poincaré, Anal. Non Lin.14 (1997) 499-552. Zbl0884.35013MR1464532
- [36] Sattinger D.H, Stability of waves of nonlinear parabolic systems, Adv. Math.22 (1976) 312-355. Zbl0344.35051MR435602
- [37] Sattinger D.H, Weighted norms for the stability of travelling waves, J. Differential Equations25 (1977) 130-144. Zbl0315.35010MR447813
- [38] Sivashinsky G.I, The structure of Bunsen flames, J. Chem. Phys.62 (1975) 638-643.
- [39] Stewart H.B, Generation of analytic semigroups by strongly elliptic operators under general boundary conditions, Trans. Amer. Math. Soc.259 (1980) 299-310. Zbl0451.35033MR561838
- [40] Williams F, Combustion Theory, Addison-Wesley, Reading, MA, 1983.
- [41] Xin J.X, Muldimensional stability of travelling waves in a bistable reaction-diffusion equation, I, Comm. Partial Differential Equations17 (1992) 1889-1899. Zbl0789.35019MR1194743
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