@article{AIHPC_2006__23_4_407_0,
author = {Berestycki, Henri and Constantin, Peter and Ryzhik, Lenya},
title = {Non-planar fronts in Boussinesq reactive flows},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
volume = {23},
year = {2006},
pages = {407-437},
doi = {10.1016/j.anihpc.2004.10.010},
mrnumber = {2245751},
zbl = {05060812},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPC_2006__23_4_407_0}
}
Berestycki, Henri; Constantin, Peter; Ryzhik, Lenya. Non-planar fronts in Boussinesq reactive flows. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) pp. 407-437. doi : 10.1016/j.anihpc.2004.10.010. http://gdmltest.u-ga.fr/item/AIHPC_2006__23_4_407_0/
[1] , , , , Front propagation in laminar flows, Phys. Rev. E 64 (2001) 6307.
[2] , , , , Front speed enhancement in cellular flows, Chaos 12 (2002) 481. | MR 1907659 | Zbl 1080.80501
[3] , , , Réaction diffusion en écoulement stationnaire rapide, C. R. Acad. Sci. Ser. IIb 328 (2000) 255-262. | Zbl 0992.76097
[4] , , , Existence of reaction-diffusion-convection waves in unbounded cylinders, Int. J. Math. Sci. 2 (2005) 169-193. | MR 2143750 | Zbl 1075.76058
[5] , The influence of advection on the propagation of fronts in reaction-diffusion equations, in: , (Eds.), Nonlinear PDEs in Condensed Matter and Reactive Flows, NATO Science Series C, vol. 569, Kluwer Academic, Doordrecht, 2003. | Zbl 1073.35113
[6] , , Front propagation in periodic excitable media, Comm. Pure Appl. Math. 55 (2002) 949-1032. | MR 1900178 | Zbl 1024.37054
[7] , , , The speed of propagation for KPP type problems. I - Periodic framework, J. Eur. Math. Soc. 7 (2005) 173-213. | MR 2127993 | Zbl 02164660
[8] , , , Elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena, Comm. Math. Phys. 253 (2005) 451-480. | MR 2140256 | Zbl 02196652
[9] , , , A nonlinear elliptic problem describing the propagation of a curved premixed flame, in: , (Eds.), Mathematical Modeling in Combustion and Related Topics, NATO ASI Series, Kluwer Academic, 1988. | MR 1011955
[10] , , , Multi-dimensional traveling wave solutions of a flame propagation model, Arch. Rational Mech. Anal. 111 (1990) 33-49. | MR 1051478 | Zbl 0711.35066
[11] , , , Traveling wave solutions to combustion models and their singular limits, SIAM J. Math. Anal. 16 (1983) 1207-1242. | MR 807905 | Zbl 0596.76096
[12] , , Traveling fronts in cylinders, Ann. Inst. H. Poincaré, Analyse Non Linéare 9 (1992) 497-572. | Numdam | MR 1191008 | Zbl 0799.35073
[13] , , , , Bulk burning rate in passive-reactive diffusion, Arch. Rational Mech. Anal. 154 (2000) 53-91. | MR 1778121 | Zbl 0979.76093
[14] , , , Fronts in reactive convection: bounds, stability and instability, Comm. Pure Appl. Math. 56 (2003) 1781-1803. | MR 2001446 | Zbl 1072.76068
[15] , Fingering of chemical fronts in porous media, Phys. Rev. Lett. 87 (2001) 054502.
[16] A. Fannjiang, A. Kiselev, L. Ryzhik, Quenching of reaction by cellular flows, Geom. Funct. Anal. (2006), in press. | MR 2221252 | Zbl 1097.35077
[17] , The wave of advance of advantageous genes, Ann. Eugenics 7 (1937) 355-369. | JFM 63.1111.04 | MR 2079
[18] , , On the propagation of concentration waves in periodic and random media, Soviet Math. Dokl. 20 (1979) 1282-1286. | MR 553200 | Zbl 0447.60060
[19] , Geometric optics approach to reaction-diffusion equations, SIAM J. Appl. Math. 46 (1986) 222-232. | MR 833475 | Zbl 0626.35047
[20] , , Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983. | MR 737190 | Zbl 0562.35001
[21] , Formules min-max pour les vitesses d'ondes progressives multidimensionnelles, Ann. Fac. Sci. Toulouse Math. 8 (6) (1999) 259-280. | Numdam | MR 1751443 | Zbl 0956.35041
[22] , , , Variational principles for propagation speeds in inhomogeneous media, SIAM J. Appl. Math. 62 (2001) 129-148. | MR 1857539 | Zbl 0995.35031
[23] , , Flame propagation and extinction in large-scale vortical flows, Combust. Flame 120 (2000) 222-232.
[24] , , , Activation energy effect on flame propagation in large-scale vortical flows, Combust. Theory Modelling 6 (2002) 479-485. | MR 1934205 | Zbl 1068.80516
[25] , , Enhancement of the travelling front speeds in reaction-diffusion equations with advection, Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (2001) 309-358. | Numdam | MR 1831659 | Zbl 1002.35069
[26] , , , Étude de l'équation de la chaleurde matière et son application à un problème biologique, Bull. Moskov. Gos. Univ. Mat. Mekh. 1 (1937) 1-25, See [31], pp. 105-130 for an English translation. | MR 278890 | Zbl 0018.32106
[27] , , Large scale front dynamics for turbulent reaction-diffusion equations with separated velocity scales, Nonlinearity 7 (1994) 1-30. | MR 1260130 | Zbl 0839.76093
[28] , , Global solutions to a reactive Boussinesq system with front data on an infinite domain, Comm. Math. Phys. 193 (1998) 287-316. | MR 1618155 | Zbl 0908.35104
[29] , Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958) 931-954. | MR 100158 | Zbl 0096.06902
[30] , , Reaction diffusion fronts in periodically layered media, J. Statist. Phys. 63 (1991) 915-932. | MR 1116041
[31] (Ed.), Dynamics of Curved Fronts, Academic Press, 1988. | MR 986791 | Zbl 0712.76009
[32] , , Problèmes de réaction-diffusion-convection dans des cylindres non bornés, C. R. Acad. Sci. Paris Sér. I Math. 333 (2001) 1077-1082. | MR 1881237 | Zbl 0991.35044
[33] , , Reaction-diffusion-convection problems in unbounded cylinders, Rev. Mat. Complut. 16 (2003) 223-276. | MR 2031883 | Zbl 1048.35034
[34] , , Model flames in the Boussinesq limit: the effects of feedback, Phys. Rev. E 67 (2003) 066305. | MR 1995905
[35] , , Location of spectrum and stability of solutions for monotone parabolic system, Adv. Differential Equations 2 (1997) 811-830. | MR 1751428 | Zbl 1023.35517
[36] , , Existence and stability of multidimensional travelling waves in the monostable case, Israel J. Math. 110 (1999) 269-292. | MR 1750434 | Zbl 0929.35064
[37] , , Spectrum of elliptic operators and stability of travelling waves, Asymptotic Anal. 23 (2000) 111-134. | MR 1771147 | Zbl 0952.35081
[38] B. Win, Ph.D. thesis, University of Chicago, 2004.
[39] , Existence of planar flame fronts in convective-diffusive periodic media, Arch. Rational Mech. Anal. 121 (1992) 205-233. | MR 1188981 | Zbl 0764.76074
[40] , Existence and nonexistence of travelling waves and reaction-diffusion front propagation in periodic media, J. Statist. Phys. 73 (1993) 893-926. | MR 1251222 | Zbl 1102.35340
[41] , Analysis and modelling of front propagation in heterogeneous media, SIAM Rev. 42 (2000) 161-230. | MR 1778352 | Zbl 0951.35060
[42] , , , , The Mathematical Theory of Combustion and Explosions, Translated from the Russian by Donald H. McNeill, Consultants Bureau [Plenum], New York, 1985. | MR 781350