Fronts in Reactive Convection: Bounds, Stability, and Instability

Communications on Pure and Applied Mathematics

Volumn 56, Issue 12, 2003, Pages 1781-1803

  Constantin, Peter ^a   Kiselev, Alexander ^b   Ryzhik, Lenya ^a  

^a UNIVERSITY OF CHICAGO   (United States)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2442536051     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/cpa.10110     Document Type: Article

References (29)

1. Berestycki, H. The influence of advection on the propagation of fronts in reaction-diffusion equations. Proceedings NATO ASI Conf. Cargese, Corsica. H. Berestycki and Y. Pomeau, eds. Kluwer, forthcoming.
2. Berestycki, H.; Hamel, F. Front propagation in periodic excitable media. Comm. Pure Appl. Math. 55 (2002), no. 8, 949-1032.
3. Berestycki, H.; Larrouturou, B.; Lions, P.-L. Multi-dimensional travelling-wave solutions of a flame propagation model. Arch. Rational Mech. Anal. 111 (1990), no. 1, 33-49.
4. Berestycki, H.; Nirenberg, L. Travelling fronts in cylinders. Ann. Inst. H. Poincaré Anal. Non Linéaire 9 (1992), no. 5, 497-572.
5. Constantin, P.; Kiselev, A.; Oberman, A.; Ryzhik, L. Bulk burning rate in passive-reactive diffusion. Arch. Ration. Mech. Anal. 154 (2000), no. 1, 53-91.
6. Constantin, P.; Kiselev, A.; Ryzhik, L. Quenching of flames by fluid advection. Comm. Pure Appl. Math. 54 (2001), no. 11, 1320-1342.
7. Chandrasekhar, S. Hydrodynamic and hydromagnetic stability. The International Series of Monographs on Physics. Clarendon, Oxford, 1961.
8. Daou, J.; Matalon, M. Flame propagation in Poiseuille flow under adiabatic conditions. Combustion and Flame 124 (2001), no. 3, 337-349.
9. Daou, J.; Matalon, M. Influence of conductive heat-losses on the propagation of premixed flames in channels. Combustion and Flame 128 (2002), no. 4, 321-339.
10. De Wit, A. Fingering of chemical fronts in porous media. Phys. Rev. Lett. 87, 054502 (2001).
11. Freidlin, M. I. Geometric optics approach to reaction-diffusion equations. SIAM J. Appl. Math. 46 (1986), no. 2, 222-232.
12. Gertner, J.; Freǐdlin, M. I. The propagation of concentration waves in periodic and random media. Dokl. Akad. Nauk SSSR 249 (1979), no. 3, 521-525; translation in Soviet Math. Dokl. 20 (1979), 1282-1286.
13. Gertner, J.; Freǐdlin, M. I. The propagation of concentration waves in periodic and random media. Dokl. Akad. Nauk SSSR 249 (1979), no. 3, 521-525; translation in Soviet Math. Dokl. 20 (1979), 1282-1286.
14. Heinze, S.; Papanicolaou, G.; Stevens, A. Variational principles for propagation speeds in inhomogeneous media. SIAM J. Appl. Math. 62 (2001), no. 1, 129-148.
15. Kagan, L.; Ronney, P. D.; Sivashinsky, G. Activation energy effect on flame propagation in large-scale vortical flows. Combust. Theory Model. 6 (2002), no. 3, 479-485.
16. Kagan, L.; Sivashinsky, G. Flame propagation and extinction in large-scale vortical flows. Combustion and Flame 120 (2000), no. 1-2, 222-232.
17. Kiselev, A.; Ryzhik, L. Enhancement of the traveling front speeds in reaction-diffusion equations with advection. Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (2001), no. 3, 309-358.
18. Majda, A. J.; Souganidis, P. E. Large-scale front dynamics for turbulent reaction-diffusion equations with separated velocity scales. Nonlinearity 7 (1994), no. 1, 1-30.
19. Malham, S.; Xin, J. X. Global solutions to a reactive Boussinesq system with front data on an infinite domain. Comm. Math. Phys. 193 (1998), no. 2, 287-316.
20. Peters, N. Turbulent combustion. Cambridge Monographs on Mechanics. Cambridge University Press, Cambridge, 2000.
21. Texier-Picard, R.; Volpert, V. Problèmes de ré action-diffusion-convection dans des cylindres non bornés. C. R. Acad. Sci. Paris Sér. I Math. 333 (2001), no. 12, 1077-1082.
22. Texier-Picard, R.; Volpert, V. Reaction-diffusion-convection problems in unbounded cylinders. Preprint, 2001.
23. Vladimirova, N.; Constantin, P.; Kiselev, A.; Ruchayskiy, O.; Ryzhik, L. Combust. Theory Model., to appear.
24. Vladimirova, N.; Rosner, R. Model flames in the Boussinesq limit: the effects of feedback. Preprint, 2002.
25. Volpert, A. I.; Volpert, V. A.; Volpert, V. A. Traveling wave solutions of parabolic systems. Translations of Mathematical Monographs, 140. American Mathematical Society, Providence, R.I., 1994.
26. Xin, J. X. Existence of planar flame fronts in convective-diffusive periodic media. Arch. Rational Mech. Anal. 121 (1992), no. 3, 205-233.
27. Xin, J. X. Existence and nonexistence of traveling waves and reaction-diffusion front propagation in periodic media. J. Statist. Phys. 73 (1993), no. 5-6, 893-926.
28. Xin, J. X. Front propagation in heterogeneous media. SIAM Rev. 42 (2000), no. 2, 161-230.
29. Y Zel'dovich, Ya. B.; Barenblatt, G. I.; Librovich, V. B.; Makhviladze, G. M. The mathematical theory of combustion and explosions. Consultants Bureau [Plenum], New York, 1985.