@article{ASENS_2004_4_37_3_469_0, author = {Hamel, Fran\c{c}ois and Monneau, R\'egis and Roquejoffre, Jean-Michel}, title = {Stability of travelling waves in a model for conical flames in two space dimensions}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {469--506}, publisher = {Elsevier}, volume = {Ser. 4, 37}, number = {3}, year = {2004}, doi = {10.1016/j.ansens.2004.03.001}, mrnumber = {2060484}, zbl = {1085.35075}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.ansens.2004.03.001/} }
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 SP - 469 EP - 506 VL - 37 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.ansens.2004.03.001/ DO - 10.1016/j.ansens.2004.03.001 LA - en ID - ASENS_2004_4_37_3_469_0 ER -
%0 Journal Article %A Hamel, François %A Monneau, Régis %A Roquejoffre, Jean-Michel %T Stability of travelling waves in a model for conical flames in two space dimensions %J Annales scientifiques de l'École Normale Supérieure %D 2004 %P 469-506 %V 37 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.ansens.2004.03.001/ %R 10.1016/j.ansens.2004.03.001 %G en %F ASENS_2004_4_37_3_469_0
Hamel, François; Monneau, Régis; Roquejoffre, Jean-Michel. Stability of travelling waves in a model for conical flames in two space dimensions. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 37 (2004) no. 3, pp. 469-506. doi : 10.1016/j.ansens.2004.03.001. http://archive.numdam.org/articles/10.1016/j.ansens.2004.03.001/
[1] Properties of solutions of ordinary differential equations in Banach space, Comm. Pure Appl. Math. 16 (1963) 121-239. | MR | Zbl
, ,[2] 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. | MR | Zbl
, ,[3] Front propagation in periodic excitable media, Comm. Pure Appl. Math. 55 (2002) 949-1032. | MR | Zbl
, ,[4] Multidimensional travelling-wave solutions of a flame propagation model, Arch. Rat. Mech. Anal. 111 (1990) 33-49. | MR | Zbl
, , ,[5] Stability of travelling fronts in a curved flame model, Part I, Linear analysis, Arch. Rat. Mech. Anal. 117 (1992) 97-117. | MR | Zbl
, , ,[6] Traveling waves solutions to combustion models and their singular limits, SIAM J. Math. Anal. 16 (6) (1985) 1207-1242. | MR | Zbl
, , ,[7] On the method of moving planes and the sliding method, Bol. Soc. Bras. Mat. 22 (1991) 1-37. | MR | Zbl
, ,[8] Travelling fronts in cylinders, Ann. Inst. H. Poincaré, Anal. Non Lin. 9 (1992) 497-572. | Numdam | MR | Zbl
, ,[9] Existence of non-planar solutions of a simple model of premixed Bunsen flames, SIAM J. Math. Anal. 31 (1999) 80-118. | MR | Zbl
, ,[10] Convergence of Solutions of the Kolmogorov Equation to Travelling Waves, in: Mem. Amer. Math. Soc., vol. 44, 1983. | MR | Zbl
,[11] On traveling wave solutions of Fisher's equation in two spatial dimensions, SIAM J. Appl. Math. 60 (2000) 371-391. | MR | Zbl
, ,[12] Lectures on Mathematical Combustion, in: CBMS-NSF Conf. Series in Applied Math., vol. 43, SIAM, 1983. | MR | Zbl
, ,[13] Fully Nonlinear Elliptic Equations, in: Colloquium Publications, Amer. Math. Soc., vol. 43, 1995. | MR | Zbl
, ,[14] User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.) 27 (1992) 1-67. | MR | Zbl
, , ,[15] Space-time behaviour in problems of hydrodynamic type: a case study, Nonlinearity 5 (6) (1992) 1265-1302. | MR | Zbl
, ,[16] Dynamics of internal layers and diffusive interfaces, in: Cbms-Nsf Regional Conference, Series in Applied Mathematics, vol. 53, 1988. | MR | Zbl
,[17] The approach of solutions of non-linear diffusion equations to travelling front solutions, Arch. Rat. Mech. Anal. 65 (1977) 335-361. | MR | Zbl
, ,[18] Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1997. | Zbl
, ,[19] Solutions of semilinear elliptic equations in RN with conical-shaped level sets, Comm. Partial Differential Equations 25 (2000) 769-819. | MR | Zbl
, ,[20] Existence and uniqueness for a free boundary problem arising in combustion theory, Interfaces Free Boundaries 4 (2002) 167-210. | MR | Zbl
, ,[21] Travelling waves and entire solutions of the Fisher-KPP equation in RN, Arch. Ration. Mech. Anal. 157 (2001) 91-163. | MR | Zbl
, ,[22] Geometric Theory of Semilinear Parabolic Equations, in: Lecture Notes in Math., Springer Verlag, New York, 1981. | MR | Zbl
,[23] On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDE's, Comm. Pure Appl. Math. 42 (1989) 15-45. | MR | Zbl
,[24] Dynamique des fronts de flammes, in: Modélisation de la combustion, Images des Mathématiques, CNRS, 1996.
,[25] Certain problems of burning-theory equations, Sov. Math. Dokl. 2 (1961) 48-51. | MR | Zbl
,[26] Stabilization of solution of the Cauchy problem for equations encountered in combustion theory, Mat. Sbornik 59 (1962) 245-288. | MR
,[27] Multidimensional stability of travelling waves in a bistable reaction-diffusion equation, II, Comm. Partial Differential Equations 17 (1992) 1901-1924. | MR | Zbl
, ,[28] Combustion, Flames and Explosions of Gases, Academic Press, New York, 1961.
, ,[29] A parabolic equation of the KPP type in higher dimensions, SIAM J. Math. Anal. 26 (1995) 1-20. | MR | Zbl
, ,[30] Pulsations in a burner-stabilized premixed plane flame, SIAM J. Appl. Math. 40 (1981) 551-562. | MR | Zbl
, ,[31] Stability of the Bunsen flame profiles in the Kuramoto-Sivashinsky equation, SIAM J. Math. Anal. 27 (1996) 765-781. | MR | Zbl
,[32] Ninomiya H., Taniguchi M., Stability of traveling curved fronts in a curvature flow with driving force, Meth. Appl. Anal., submitted for publication. | MR | Zbl
[33] Stability of travelling fronts in a curved flame model, Part II: Non-linear orbital stability, Arch. Rat. Mech. Anal. 117 (1992) 119-153. | MR | Zbl
,[34] Convergence to travelling waves for solutions of a class of semilinear parabolic equation, J. Differential Equations 108 (1994) 262-295. | MR | Zbl
,[35] 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. | Numdam | MR | Zbl
,[36] Stability of waves of nonlinear parabolic systems, Adv. Math. 22 (1976) 312-355. | MR | Zbl
,[37] Weighted norms for the stability of travelling waves, J. Differential Equations 25 (1977) 130-144. | MR | Zbl
,[38] The structure of Bunsen flames, J. Chem. Phys. 62 (1975) 638-643.
,[39] Generation of analytic semigroups by strongly elliptic operators under general boundary conditions, Trans. Amer. Math. Soc. 259 (1980) 299-310. | MR | Zbl
,[40] Combustion Theory, Addison-Wesley, Reading, MA, 1983.
,[41] Muldimensional stability of travelling waves in a bistable reaction-diffusion equation, I, Comm. Partial Differential Equations 17 (1992) 1889-1899. | MR | Zbl
,Cité par Sources :