Non-planar fronts in Boussinesq reactive flows
Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 4, pp. 407-437.
@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},
     pages = {407--437},
     publisher = {Elsevier},
     volume = {23},
     number = {4},
     year = {2006},
     doi = {10.1016/j.anihpc.2004.10.010},
     zbl = {05060812},
     mrnumber = {2245751},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2004.10.010/}
}
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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) no. 4, pp. 407-437. doi : 10.1016/j.anihpc.2004.10.010. http://www.numdam.org/articles/10.1016/j.anihpc.2004.10.010/

[1] Abel M., Celani A., Vergni D., Vulpiani A., Front propagation in laminar flows, Phys. Rev. E 64 (2001) 6307.

[2] Abel M., Cencini M., Vergni D., Vulpiani A., Front speed enhancement in cellular flows, Chaos 12 (2002) 481. | MR 1907659 | Zbl 1080.80501

[3] Audoly B., Berestycki H., Pomeau Y., Réaction diffusion en écoulement stationnaire rapide, C. R. Acad. Sci. Ser. IIb 328 (2000) 255-262. | Zbl 0992.76097

[4] Belk M., Kazmierczak B., Volpert V., Existence of reaction-diffusion-convection waves in unbounded cylinders, Int. J. Math. Sci. 2 (2005) 169-193. | MR 2143750 | Zbl 1075.76058

[5] Berestycki H., The influence of advection on the propagation of fronts in reaction-diffusion equations, in: Berestycki H., Pomeau Y. (Eds.), Nonlinear PDEs in Condensed Matter and Reactive Flows, NATO Science Series C, vol. 569, Kluwer Academic, Doordrecht, 2003. | Zbl 1073.35113

[6] Berestycki H., Hamel F., Front propagation in periodic excitable media, Comm. Pure Appl. Math. 55 (2002) 949-1032. | MR 1900178 | Zbl 1024.37054

[7] Berestycki H., Hamel F., Nadirashvili N., The speed of propagation for KPP type problems. I - Periodic framework, J. Eur. Math. Soc. 7 (2005) 173-213. | MR 2127993 | Zbl 02164660

[8] Berestycki H., Hamel F., Nadirashvili N., Elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena, Comm. Math. Phys. 253 (2005) 451-480. | MR 2140256 | Zbl 02196652

[9] Berestycki H., Larrouturou B., Nirenberg L., A nonlinear elliptic problem describing the propagation of a curved premixed flame, in: Brauner C.-M., Schmidt-Lainé C. (Eds.), Mathematical Modeling in Combustion and Related Topics, NATO ASI Series, Kluwer Academic, 1988. | MR 1011955

[10] Berestycki H., Larrouturou B., Lions P.L., Multi-dimensional traveling wave solutions of a flame propagation model, Arch. Rational Mech. Anal. 111 (1990) 33-49. | MR 1051478 | Zbl 0711.35066

[11] Berestycki H., Nicolaenco B., Scheurer B., Traveling wave solutions to combustion models and their singular limits, SIAM J. Math. Anal. 16 (1983) 1207-1242. | MR 807905 | Zbl 0596.76096

[12] Berestycki H., Nirenberg L., Traveling fronts in cylinders, Ann. Inst. H. Poincaré, Analyse Non Linéare 9 (1992) 497-572. | Numdam | MR 1191008 | Zbl 0799.35073

[13] Constantin P., Kiselev A., Oberman A., Ryzhik L., Bulk burning rate in passive-reactive diffusion, Arch. Rational Mech. Anal. 154 (2000) 53-91. | MR 1778121 | Zbl 0979.76093

[14] Constantin P., Kiselev A., Ryzhik L., Fronts in reactive convection: bounds, stability and instability, Comm. Pure Appl. Math. 56 (2003) 1781-1803. | MR 2001446 | Zbl 1072.76068

[15] De Wit A., 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] Fisher R., The wave of advance of advantageous genes, Ann. Eugenics 7 (1937) 355-369. | JFM 63.1111.04 | MR 2079

[18] Freidlin M., Gärtner J., On the propagation of concentration waves in periodic and random media, Soviet Math. Dokl. 20 (1979) 1282-1286. | MR 553200 | Zbl 0447.60060

[19] Freidlin M., Geometric optics approach to reaction-diffusion equations, SIAM J. Appl. Math. 46 (1986) 222-232. | MR 833475 | Zbl 0626.35047

[20] Gilbarg D., Trudinger , Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983. | MR 737190 | Zbl 0562.35001

[21] Hamel F., 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] Heinze S., Papanicolaou G., Stevens A., Variational principles for propagation speeds in inhomogeneous media, SIAM J. Appl. Math. 62 (2001) 129-148. | MR 1857539 | Zbl 0995.35031

[23] Kagan L., Sivashinsky G., Flame propagation and extinction in large-scale vortical flows, Combust. Flame 120 (2000) 222-232.

[24] Kagan L., Ronney P.D., Sivashinsky G., Activation energy effect on flame propagation in large-scale vortical flows, Combust. Theory Modelling 6 (2002) 479-485. | MR 1934205 | Zbl 1068.80516

[25] Kiselev A., Ryzhik L., 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] Kolmogorov A.N., Petrovskii I.G., Piskunov N.S., 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] Majda A., Souganidis P., Large scale front dynamics for turbulent reaction-diffusion equations with separated velocity scales, Nonlinearity 7 (1994) 1-30. | MR 1260130 | Zbl 0839.76093

[28] Malham S., Xin J., 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] Nash J., Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958) 931-954. | MR 100158 | Zbl 0096.06902

[30] Papanicolaou G., Xin X., Reaction diffusion fronts in periodically layered media, J. Statist. Phys. 63 (1991) 915-932. | MR 1116041

[31] Pelcé P. (Ed.), Dynamics of Curved Fronts, Academic Press, 1988. | MR 986791 | Zbl 0712.76009

[32] Texier-Picard R., Volpert V., 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] Texier-Picard R., Volpert V., Reaction-diffusion-convection problems in unbounded cylinders, Rev. Mat. Complut. 16 (2003) 223-276. | MR 2031883 | Zbl 1048.35034

[34] Vladimirova N., Rosner R., Model flames in the Boussinesq limit: the effects of feedback, Phys. Rev. E 67 (2003) 066305. | MR 1995905

[35] Volpert V.A., Volpert A.I., Location of spectrum and stability of solutions for monotone parabolic system, Adv. Differential Equations 2 (1997) 811-830. | MR 1751428 | Zbl 1023.35517

[36] Volpert V.A., Volpert A.I., Existence and stability of multidimensional travelling waves in the monostable case, Israel J. Math. 110 (1999) 269-292. | MR 1750434 | Zbl 0929.35064

[37] Volpert V.A., Volpert A.I., 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] Xin J., Existence of planar flame fronts in convective-diffusive periodic media, Arch. Rational Mech. Anal. 121 (1992) 205-233. | MR 1188981 | Zbl 0764.76074

[40] Xin J., 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] Xin J., Analysis and modelling of front propagation in heterogeneous media, SIAM Rev. 42 (2000) 161-230. | MR 1778352 | Zbl 0951.35060

[42] Zeldovich Ya.B., Barenblatt G.I., Librovich V.B., Makhviladze G.M., The Mathematical Theory of Combustion and Explosions, Translated from the Russian by Donald H. McNeill, Consultants Bureau [Plenum], New York, 1985. | MR 781350

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