Non-planar fronts in Boussinesq reactive flows

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

Volumn 23, Issue 4, 2006, Pages 407-437

  Berestycki, Henri ^a   Constantin, Peter ^b   Ryzhik, Lenya ^b  

^a ÉCOLE DES HAUTES ÉTUDES EN SCIENCES SOCIALES   (France)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CYLINDERS (CONTAINERS); NUMERICAL METHODS;

BOUSSINESQ EQUATIONS; CAUCHY PROBLEM; NON-PLANAR TRAVELING FRONT SOLUTIONS; RAYLEIGH NUMBER;

FLOW OF FLUIDS;

EID: 33745727249     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2004.10.010     Document Type: Article

References (42)

1. Abel M., Celani A., Vergni D., and Vulpiani A. Front propagation in laminar flows. Phys. Rev. E 64 (2001) 6307
2. Abel M., Cencini M., Vergni D., and Vulpiani A. Front speed enhancement in cellular flows. Chaos 12 (2002) 481
3. Audoly B., Berestycki H., and Pomeau Y. Réaction diffusion en écoulement stationnaire rapide. C. R. Acad. Sci. Ser. IIb 328 (2000) 255-262
4. Belk M., Kazmierczak B., and Volpert V. Existence of reaction-diffusion-convection waves in unbounded cylinders. Int. J. Math. Sci. 2 (2005) 169-193
5. Berestycki H. The influence of advection on the propagation of fronts in reaction-diffusion equations. In: Berestycki H., and Pomeau Y. (Eds). Nonlinear PDEs in Condensed Matter and Reactive Flows. NATO Science Series C vol. 569 (2003), Kluwer Academic, Doordrecht
6. Berestycki H., and Hamel F. Front propagation in periodic excitable media. Comm. Pure Appl. Math. 55 (2002) 949-1032
7. Berestycki H., Hamel F., and Nadirashvili N. The speed of propagation for KPP type problems. I - Periodic framework. J. Eur. Math. Soc. 7 (2005) 173-213
8. Berestycki H., Hamel F., and Nadirashvili N. Elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena. Comm. Math. Phys. 253 (2005) 451-480
9. Berestycki H., Larrouturou B., and Nirenberg L. A nonlinear elliptic problem describing the propagation of a curved premixed flame. In: Brauner C.-M., and Schmidt-Lainé C. (Eds). Mathematical Modeling in Combustion and Related Topics. NATO ASI Series (1988), Kluwer Academic
10. Berestycki H., Larrouturou B., and Lions P.L. Multi-dimensional traveling wave solutions of a flame propagation model. Arch. Rational Mech. Anal. 111 (1990) 33-49
11. Berestycki H., Nicolaenco B., and Scheurer B. Traveling wave solutions to combustion models and their singular limits. SIAM J. Math. Anal. 16 (1983) 1207-1242
12. Berestycki H., and Nirenberg L. Traveling fronts in cylinders. Ann. Inst. H. Poincaré, Analyse Non Linéare 9 (1992) 497-572
13. Constantin P., Kiselev A., Oberman A., and Ryzhik L. Bulk burning rate in passive-reactive diffusion. Arch. Rational Mech. Anal. 154 (2000) 53-91
14. Constantin P., Kiselev A., and Ryzhik L. Fronts in reactive convection: bounds, stability and instability. Comm. Pure Appl. Math. 56 (2003) 1781-1803
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
17. Fisher R. The wave of advance of advantageous genes. Ann. Eugenics 7 (1937) 355-369
18. Freidlin M., and Gärtner J. On the propagation of concentration waves in periodic and random media. Soviet Math. Dokl. 20 (1979) 1282-1286
19. Freidlin M. Geometric optics approach to reaction-diffusion equations. SIAM J. Appl. Math. 46 (1986) 222-232
20. Gilbarg D., and Trudinger. Elliptic Partial Differential Equations of Second Order (1983), Springer-Verlag
21. Hamel F. Formules min-max pour les vitesses d'ondes progressives multidimensionnelles. Ann. Fac. Sci. Toulouse Math. 8 6 (1999) 259-280
22. Heinze S., Papanicolaou G., and Stevens A. Variational principles for propagation speeds in inhomogeneous media. SIAM J. Appl. Math. 62 (2001) 129-148
23. Kagan L., and Sivashinsky G. Flame propagation and extinction in large-scale vortical flows. Combust. Flame 120 (2000) 222-232
24. Kagan L., Ronney P.D., and Sivashinsky G. Activation energy effect on flame propagation in large-scale vortical flows. Combust. Theory Modelling 6 (2002) 479-485
25. Kiselev A., and 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
26. Kolmogorov A.N., Petrovskii I.G., and 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
27. Majda A., and Souganidis P. Large scale front dynamics for turbulent reaction-diffusion equations with separated velocity scales. Nonlinearity 7 (1994) 1-30
28. Malham S., and Xin J. Global solutions to a reactive Boussinesq system with front data on an infinite domain. Comm. Math. Phys. 193 (1998) 287-316
29. Nash J. Continuity of solutions of parabolic and elliptic equations. Amer. J. Math. 80 (1958) 931-954
30. Papanicolaou G., and Xin X. Reaction diffusion fronts in periodically layered media. J. Statist. Phys. 63 (1991) 915-932
31. In: Pelcé P. (Ed). Dynamics of Curved Fronts (1988), Academic Press
32. Texier-Picard R., and Volpert V. Problèmes de réaction-diffusion-convection dans des cylindres non bornés. C. R. Acad. Sci. Paris Sér. I Math. 333 (2001) 1077-1082
33. Texier-Picard R., and Volpert V. Reaction-diffusion-convection problems in unbounded cylinders. Rev. Mat. Complut. 16 (2003) 223-276
34. Vladimirova N., and Rosner R. Model flames in the Boussinesq limit: the effects of feedback. Phys. Rev. E 67 (2003) 066305
35. Volpert V.A., and Volpert A.I. Location of spectrum and stability of solutions for monotone parabolic system. Adv. Differential Equations 2 (1997) 811-830
36. Volpert V.A., and Volpert A.I. Existence and stability of multidimensional travelling waves in the monostable case. Israel J. Math. 110 (1999) 269-292
37. Volpert V.A., and Volpert A.I. Spectrum of elliptic operators and stability of travelling waves. Asymptotic Anal. 23 (2000) 111-134
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
40. Xin J. Existence and nonexistence of travelling waves and reaction-diffusion front propagation in periodic media. J. Statist. Phys. 73 (1993) 893-926
41. Xin J. Analysis and modelling of front propagation in heterogeneous media. SIAM Rev. 42 (2000) 161-230
42. Zeldovich Ya.B., Barenblatt G.I., Librovich V.B., and Makhviladze G.M. The Mathematical Theory of Combustion and Explosions. Translated from the Russian by Donald H. McNeill (1985), Consultants Bureau [Plenum], New York