@article{AIHPC_2001__18_3_309_0, author = {Kiselev, Alexander and Ryzhik, Leonid}, title = {Enhancement of the traveling front speeds in reaction-diffusion equations with advection}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {309--358}, publisher = {Elsevier}, volume = {18}, number = {3}, year = {2001}, mrnumber = {1831659}, zbl = {1002.35069}, language = {en}, url = {http://www.numdam.org/item/AIHPC_2001__18_3_309_0/} }
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 SP - 309 EP - 358 VL - 18 IS - 3 PB - Elsevier UR - http://www.numdam.org/item/AIHPC_2001__18_3_309_0/ LA - en ID - AIHPC_2001__18_3_309_0 ER -
%0 Journal Article %A Kiselev, Alexander %A Ryzhik, Leonid %T Enhancement of the traveling front speeds in reaction-diffusion equations with advection %J Annales de l'I.H.P. Analyse non linéaire %D 2001 %P 309-358 %V 18 %N 3 %I Elsevier %U http://www.numdam.org/item/AIHPC_2001__18_3_309_0/ %G en %F AIHPC_2001__18_3_309_0
Kiselev, Alexander; Ryzhik, Leonid. Enhancement of the traveling front speeds in reaction-diffusion equations with advection. Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) no. 3, pp. 309-358. http://www.numdam.org/item/AIHPC_2001__18_3_309_0/
[1] Audoly B., Berestycki H., Pomeau Y., Reaction-diffusion in fast steady flow, C.R. Acad. Sci., Ser. IIB, 328, 255-262. | Zbl
[2] Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978. | MR | Zbl
, , ,[3] Berestycki H., Hamel F., Propagation of flames through vortical cells, preprint.
[4] Multi-dimensional traveling wave solutions of a flame propagation model, Arch. Rational Mech. Anal 111 (1990) 33-49. | MR | Zbl
, , ,[5] Stability of traveling fronts in a model for flame propagation I: linear stability, Arch. Rational Mech. Anal. 117 (1992) 97-117. | MR | Zbl
, , ,[6] Some qualitative properties of solutions of semilinear equations in cylindrical domains, in: , (Eds.), Analysis etc., Academic Press, 1990, pp. 115-164. | MR | Zbl
, ,[7] Traveling fronts in cylinders, Annales de l'IHP, Analyse non linéare 9 (1992) 497-572. | Numdam | MR | Zbl
, ,[8] Theory of pre-mixed flame propagation in large-scale turbulence, J. Fluid. Mech. 90 (1979) 589-604. | Zbl
, ,[9] Bulk burning rate in passive-reactive diffusion, Arch. Rat. Mech. Anal. 154 (2000) 53-91. | MR | Zbl
, , , ,[10] Comparison of turbulent flame speeds from complete averaging and the G-equation, Phys. Fluids. 7 (1995) 2052-2060. | MR | Zbl
, , ,[11] Effective geometric from dynamics for premixed turbulent combustion with separated velocity scales, Combust. Sci. Tech. 103 (1994) 85.
, , ,[12] Convection enhanced diffusion for periodic flows, SIAM J. Appl. Math. 54 (1994) 333-408. | MR | Zbl
, ,[13] The wave of advance of advantageous genes, Ann. Eugenics 7 (1937) 355-369. | JFM
,[14] On the propagation of concentration waves in periodic and random media, Soviet Math. Dokl. 20 (1979) 1282-1286. | MR | Zbl
, ,[15] Geometric optics approach to reaction-diffusion equations, SIAM J. Appl. Math. 46 (1986) 222-232. | MR | Zbl
,[16] Limit theorems for large deviations and reaction-diffusion equations, Ann. Probab. 13 (1985) 639-675. | MR | Zbl
,[17] Formules min-max pour les vitesses d'ondes progressives multidimensionnelles, Ann. Fac. Sci., Toulouse Math. (6) 8 (1999) 259-280. | Numdam | MR | Zbl
,[18] Heinze S., Papanicolaou G., Stevens A., Variational principles for propagation speeds in inhomogeneous media, SIAM J. Appl. Math., to appear. | MR | Zbl
[19] Phys. Rev. Lett. 68 (1992) 934.
, ,[20] Simple derivation of Yakhot's turbulent premixed flame speed formula, Combust. Sci. Tech. 60 (1988) 163-165.
,[21] On flame extinction by a spatially periodic shear flow, Combust. Theor. Model. 2 (1998) 399-404. | Zbl
, , ,[22] On flame propagation and extinction in large scale vortical flows, Combustion and Flame 120 (2000) 222-232.
, ,[23] 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] Large scale front dynamics for turbulent reaction-diffusion equations with separated velocity scales, Nonlinearity 7 (1994) 1-30. | MR | Zbl
, ,[25] A parabolic equation of the KPP type in higher dimensions, SIAM J. Math. Anal. 26 (1995) 1-20. | MR | Zbl
, ,[26] The effect of finite front thickness on the enhanced speed of propagation, Combust. Sci. Tech. 129 (1997) 89-112.
, ,[27] Dynamics of Curved Fronts, Academic Press, 1988. | MR | Zbl
(Ed.),[28] Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1967. | MR | Zbl
, ,[29] Some open issues in premixed turbulent combustion, in: , (Eds.), Modeling in Combustion Science, Springer-Verlag, Berlin, 1995.
,[30] Stability of traveling fronts in a model for flame propagation II: nonlinear stability, Arch. Rat. Mech. Anal. 117 (1992) 119-153. | MR | Zbl
,[31] Existence of planar flame fronts in convective-diffusive periodic media, Arch. Rat. Mech. Anal. 121 (1992) 205-233. | MR | Zbl
,[32] Existence and nonexistence of traveling waves and reaction-diffusion front propagation in periodic media, J. Stat. Phys. 73 (1993) 893-926. | MR | Zbl
,[33] Analysis and modeling of front propagation in heterogeneous media, SIAM Review 42 (2000) 161-230. | MR | Zbl
,[34] Yakhot V., Propagation velocity of premixed turbulent flames, Combust. Sci. Tech. 60, 191-214.