Enhancement of the traveling front speeds in reaction-diffusion equations with advection

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 18, Issue 3, 2001, Pages 309-358

  Kiselev, Alexander ^a   Ryzhik, Leonid ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346449878     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(01)00068-3     Document Type: Article

References (34)

1. Audoly B., Berestycki H., Pomeau Y., Reaction-diffusion in fast steady flow, C.R. Acad. Sci., Ser. IIB, 328, 255-262.
2. Bensoussan A., Lions J.L., Papanicolaou G., Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978.
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. Anal 111 (1990) 33-49.
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.
6. Berestycki H., Nirenberg L., Some qualitative properties of solutions of semilinear equations in cylindrical domains, in: Rabinowitz P et al. (Eds.), Analysis etc., Academic Press, 1990, pp. 115-164.
7. Berestycki H., Nirenberg L., Traveling fronts in cylinders, Annales de 1'IHP, Analyse non lineare 9 (1992) 497-572.
8. Clavin P., Williams F.A., Theory of pre-mixed flame propagation in large-scale turbulence, J. Fluid. Mech. 90 (1979) 589-604.
9. Constantin P., Kiselev A., Oberman A., Ryzhik L., Bulk burning rate in passive-reactive diffusion, Arch. Rat. Mech. Anal. 154 (2000) 53-91.
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.
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.
13. Fisher R., The wave of advance of advantageous genes, Ann. Eugenics 7 (1937) 355-369.
14. Freidlin M., Gärtner J., On the propagation of concentration waves in periodic and random media, Soviet Math. Dokl. 20 (1979) 1282-1286.
15. Freidlin M., Geometric optics approach to reaction-diffusion equations, SIAM J. Appl. Math. 46 (1986) 222-232.
16. Freidlin M., Limit theorems for large deviations and reaction-diffusion equations, Ann. Probab. 13 (1985) 639-675.
17. Hamel F., Formules min-max pour les vitesses d'ondes progressives multidimensionnelles, Ann. Fac. Sci., Toulouse Math. (6) 8 (1999) 259-280.
18. Heinze S., Papanicolaou G., Stevens A., Variational principles for propagation speeds in inhomogeneous media, SIAM J. Appl. Math., to appear.
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.
22. Kagan L., Sivashinsky G., On flame propagation and extinction in large scale vortical flows, Combustion and Flame 120 (2000) 222-232.
23. Kolmogorov A.N., Petrovskii I.G., Piskunov N.S., Étude de l'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, Nonlinearity 7 (1994) 1-30.
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.
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.
28. Protter M., Weinberger H., Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1967.
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.
31. Xin J., Existence of planar flame fronts in convective-diffusive periodic media, Arch. Rat. Mech. Anal. 121 (1992) 205-233.
32. Xin J., Existence and nonexistence of traveling waves and reaction-diffusion front propagation in periodic media, J. Stat. Phys. 73 (1993) 893-926.
33. Xin J., Analysis and modeling of front propagation in heterogeneous media, SIAM Review 42 (2000) 161-230.
34. Yakhot V., Propagation velocity of premixed turbulent flames, Combust. Sci. Tech. 60, 191-214.