Enhancement of the traveling front speeds in reaction-diffusion equations with advection
Alexander Kiselev; Leonid Ryzhik
Annales de l'I.H.P. Analyse non linéaire (2001)
- Volume: 18, Issue: 3, page 309-358
- ISSN: 0294-1449
Access Full Article
topHow to cite
topKiselev, Alexander, and Ryzhik, Leonid. "Enhancement of the traveling front speeds in reaction-diffusion equations with advection." Annales de l'I.H.P. Analyse non linéaire 18.3 (2001): 309-358. <http://eudml.org/doc/78523>.
@article{Kiselev2001,
author = {Kiselev, Alexander, Ryzhik, Leonid},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {ambient fluid flow; percolating flows; cellular flows},
language = {eng},
number = {3},
pages = {309-358},
publisher = {Elsevier},
title = {Enhancement of the traveling front speeds in reaction-diffusion equations with advection},
url = {http://eudml.org/doc/78523},
volume = {18},
year = {2001},
}
TY - JOUR
AU - Kiselev, Alexander
AU - Ryzhik, Leonid
TI - Enhancement of the traveling front speeds in reaction-diffusion equations with advection
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2001
PB - Elsevier
VL - 18
IS - 3
SP - 309
EP - 358
LA - eng
KW - ambient fluid flow; percolating flows; cellular flows
UR - http://eudml.org/doc/78523
ER -
References
top- [1] Audoly B., Berestycki H., Pomeau Y., Reaction-diffusion in fast steady flow, C.R. Acad. Sci., Ser. IIB, 328, 255–262. Zbl0992.76097
- [2] Bensoussan A, Lions J.L, Papanicolaou G, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978. Zbl0404.35001MR503330
- [3] Berestycki H., Hamel F., Propagation of flames through vortical cells, preprint.
- [4] Berestycki H, Larrouturou B, Lions P.L, Multi-dimensional traveling wave solutions of a flame propagation model, Arch. Rational Mech. Anal111 (1990) 33-49. Zbl0711.35066MR1051478
- [5] Berestycki H, Larrouturou B, Roquejoffre J.-M, Stability of traveling fronts in a model for flame propagation I: linear stability, Arch. Rational Mech. Anal.117 (1992) 97-117. Zbl0763.76033MR1145107
- [6] Berestycki H, Nirenberg L, Some qualitative properties of solutions of semilinear equations in cylindrical domains, in: Rabinowitz P, (Eds.), Analysis etc., Academic Press, 1990, pp. 115-164. Zbl0705.35004MR1039342
- [7] Berestycki H, Nirenberg L, Traveling fronts in cylinders, Annales de l'IHP, Analyse non linéare9 (1992) 497-572. Zbl0799.35073MR1191008
- [8] Clavin P, Williams F.A, Theory of pre-mixed flame propagation in large-scale turbulence, J. Fluid. Mech.90 (1979) 589-604. Zbl0434.76052
- [9] Constantin P, Kiselev A, Oberman A, Ryzhik L, Bulk burning rate in passive-reactive diffusion, Arch. Rat. Mech. Anal.154 (2000) 53-91. Zbl0979.76093MR1778121
- [10] Embid P, Majda A, Souganidis P, Comparison of turbulent flame speeds from complete averaging and the G-equation, Phys. Fluids.7 (1995) 2052-2060. Zbl1039.80504MR1346082
- [11] Embid P, Majda A, Souganidis P, Effective geometric from dynamics for premixed turbulent combustion with separated velocity scales, Combust. Sci. Tech.103 (1994) 85.
- [12] Fannjiang A, Papanicolaou G, Convection enhanced diffusion for periodic flows, SIAM J. Appl. Math.54 (1994) 333-408. Zbl0796.76084MR1265233
- [13] Fisher R, The wave of advance of advantageous genes, Ann. Eugenics7 (1937) 355-369. Zbl63.1111.04JFM63.1111.04
- [14] Freidlin M, Gärtner J, On the propagation of concentration waves in periodic and random media, Soviet Math. Dokl.20 (1979) 1282-1286. Zbl0447.60060MR553200
- [15] Freidlin M, Geometric optics approach to reaction-diffusion equations, SIAM J. Appl. Math.46 (1986) 222-232. Zbl0626.35047MR833475
- [16] Freidlin M, Limit theorems for large deviations and reaction-diffusion equations, Ann. Probab.13 (1985) 639-675. Zbl0576.60070MR799415
- [17] Hamel F, Formules min-max pour les vitesses d'ondes progressives multidimensionnelles, Ann. Fac. Sci., Toulouse Math. (6)8 (1999) 259-280. Zbl0956.35041MR1751443
- [18] Heinze S., Papanicolaou G., Stevens A., Variational principles for propagation speeds in inhomogeneous media, SIAM J. Appl. Math., to appear. Zbl0995.35031MR1857539
- [19] Kerstein A, Ashurst W, Phys. Rev. Lett.68 (1992) 934.
- [20] Kerstein A, Simple derivation of Yakhot's turbulent premixed flame speed formula, Combust. Sci. Tech.60 (1988) 163-165.
- [21] Kagan L, Sivashinsky G, Makhviladze G, On flame extinction by a spatially periodic shear flow, Combust. Theor. Model.2 (1998) 399-404. Zbl0944.76093
- [22] Kagan L, Sivashinsky G, On flame propagation and extinction in large scale vortical flows, Combustion and Flame120 (2000) 222-232.
- [23] Kolmogorov A.N, Petrovskii I.G, Piskunov N.S, Étude de I'équation de la chaleurde matiére et son application à un problème biologique, Bull. Moskov. Gos. Univ. Mat. Mekh.1 (1937) 1-25, (see [27] pp. 105–130 for an English transl.).
- [24] Majda A, Souganidis P, Large scale front dynamics for turbulent reaction-diffusion equations with separated velocity scales, Nonlinearity7 (1994) 1-30. Zbl0839.76093MR1260130
- [25] 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
- [26] McLaughlin R, Zhu J, The effect of finite front thickness on the enhanced speed of propagation, Combust. Sci. Tech.129 (1997) 89-112.
- [27] Pelcé P (Ed.), Dynamics of Curved Fronts, Academic Press, 1988. Zbl0712.76009MR986791
- [28] Protter M, Weinberger H, Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1967. Zbl0153.13602MR219861
- [29] Ronney P, Some open issues in premixed turbulent combustion, in: Buckmuster J, Takeno T (Eds.), Modeling in Combustion Science, Springer-Verlag, Berlin, 1995.
- [30] Roquejoffre J.-M, Stability of traveling fronts in a model for flame propagation II: nonlinear stability, Arch. Rat. Mech. Anal.117 (1992) 119-153. Zbl0763.76034MR1145108
- [31] Xin J, Existence of planar flame fronts in convective-diffusive periodic media, Arch. Rat. Mech. Anal.121 (1992) 205-233. Zbl0764.76074MR1188981
- [32] Xin J, Existence and nonexistence of traveling waves and reaction-diffusion front propagation in periodic media, J. Stat. Phys.73 (1993) 893-926. Zbl1102.35340MR1251222
- [33] Xin J, Analysis and modeling of front propagation in heterogeneous media, SIAM Review42 (2000) 161-230. Zbl0951.35060MR1778352
- [34] Yakhot V., Propagation velocity of premixed turbulent flames, Combust. Sci. Tech. 60, 191–214.
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.