Quenching of reaction by cellular flows

Geometric and Functional Analysis

Volumn 16, Issue 1, 2006, Pages 40-69

  Fannjiang, A ^a   Kiselev, A ^b,c   Ryzhik, L ^d  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b INSTITUTE FOR ADVANCED STUDY   (United States)

^c UNIVERSITY OF WISCONSIN MADISON   (United States)

^d UNIVERSITY OF CHICAGO   (United States)

Author keywords

Cellular flow; Combustion; Quenching; Reaction diffusion

Indexed keywords

EID: 33646485810     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-006-0554-y     Document Type: Article

References (38)

1. [ACVV1] M. ABEL, A. CELANI, D. VERGNI, A. VULPIANI, Front propagation in laminar flows, Physical Review E 64 (2001), 046307.
2. [ACVV2] M. ABEL, M. CENCINI, D. VERGNI, A. VULPIANI, Front speed enhancement in cellular flows, Chaos 12 (2003), 481.
3. [AuBP] B. AUDOLY, H. BERESTYCKI, Y. POMEAU, Réaction-diffusion en écoulement stationnaire rapide, C.R. Acad. Sci. Paris 328 II (2000), 255-262.
4. [B] H. BERESTYCKI, The influence of advection on the propagation of fronts in reaction-diffusion equations, in "Nonlinear PDEs in Condensed Matter and Reactive Flows", (H. Berestycki, Y. Pomeau, eds.) NATO Science Series C 569, Kluwer, Dordrecht (2002), 11-48.
5. [BH] H. BERESTYCKI, F. HAMEL, Front propagation in periodic excitable media, Comm. Pure Appl. Math. 55 (2002), 949-1032.
6. [BLL] H. BERESTYCKI, B. LARROUTUROU, P.-L. LIONS, Multi-dimensional traveling wave solutions of a flame propagation model, Arch. Rational Mech. Anal. 111, (1990), 33-49.
7. [BN] H. BERESTYCKI, L. NIRENBERG, Traveling fronts in cylinders, Annales de l'IHP, Analyse non linéare 9 (1992), 497-572.
8. [C] S. CHILDRESS, Alpha-effect in flux ropes and sheets, Phys. Earth Planet Inter. 20 (1979), 172-180.
9. [CoKOR] P. CONSTANTIN, A. KISELEV, A. OBERMAN, L. RYZHIK, Bulk burning rate in passive-reactive diffusion, Arch. Rat. Mech. Anal. 154 (2000), 53-91.
10. [CoKR] P. CONSTANTIN, A. KISELEV, L. RYZHIK, Quenching of flames by fluid advection, Comm. Pure Appl. Math 54 (2001), 1320-1342.
11. [FP] A. FANNJIANG, G. PAPANICOLAOU, Convection enhanced diffusion for periodic flows, SIAM Jour. Appl. Math. 54 (1994), 333-408.
12. [Fr1] M. FREIDLIN, Functional Integration and Partial Differential Equations, Princeton University Press, Princeton 1985.
13. [Fr2] M. FREIDLIN, Reaction-diffusion in incompressible fluid: asymptotic problems, J. Diff. Eq. 179 (2002), 44-96.
14. [FrW1] M. FREIDLIN, A. WENTZELL, Random Perturbations of Hamiltonian Systems, Memoir AMS, 1994.
15. [FrW2] M. FREIDLIN, A. WENTZELL, Random Perturbations of Dynamical Systems, 2nd ed., Springer-Verlag, New York/Berlin, 1998.
16. [H] S. HEINZE, Large convection limits for KPP fronts, preprint (2005).
17. [KS] L. KAGAN, G. SIVASHINSKY, Flame propagation and extinction in large-scale vortical flows, Combust. Flame 120 (2000), 222-232.
18. [KRS] L. KAGAN, P.D. RONNEY, G. SIVASHINSKY, Activation energy effect on flame propagation in large-scale vortical flows, Combust. Theory Modelling 6 (2002), 479-485.
19. [Ka] YA. KANEL, Stabilization of solutions of the Cauchy problem for equations encountered in combustion theory, Mat. Sbornik 59 (1962), 245-288.
20. [KhBM] B. KHOUDIER, A. BOURLIOUX, A. MAJDA, Parametrizing the burning rate speed enhancement by small scale periodic flows: I. Unsteady shears, flame residence time and bending, Combust. Theory Model. 5 (2001), 295-318.
21. [KiR] A. KISELEV, L. RYZHIK, Enhancement of the traveling front speeds in reaction-diffusion equations with advection, Ann. de l'Inst. Henri Poincaré, C. Analyse non linéaire 18 (2001), 309-358.
22. [KiZ] A. KISELEV, A. ZLATOS, Quenching of combustion by shear flows, Duke Math. J., to appear.
23. [KisMN] I. KISS, J. MERKIN, Z. NEUFELD, Combustion initiation and extinction in a 2D chaotic flow, Phys, D. 183 (2003), 175-189.
24. [Kis+] I. KISS, J. MERKIN, S. SCOTT, P. SIMON, S. KALLIADASIS, Z. NEUFELD, The structure of flame filaments in chaotic flows. Phys. D. 176 (2003), 67-81.
25. [Ko] L. KORALOV, Random perturbations of two-dimensional Hamiltonian flows, Prob. Theor. Rel. Fields 129 (2004), 37-62.
26. [KM] P. KRAMER, A. MAJDA, Simplified models for turbulent diffusion: theory, numerical modelling, and physical phenomena, Phys. Rep. 314 (1999), 237-574.
27. [N] J. NASH, Continuity of solutions of parabolic and elliptic equations, Amer. Jour. Math. 80 (1958), 931-954.
28. [NoPR] A. NOVIKOV, G. PAPANICOLAOU, L. RYZHIK, Boundary layers for cellular flows at high Péclet numbers, Comm. Pure Appl. Math. 58 (2005), 867-922.
29. [NoR] A. NOVIKOV, L. RYZHIK, Bounds on the speed of propagation of the KPP fronts in a cellular flow, preprint (2004).
30. [O] B. OKSENDAL, Stochastic Differential Equations, Springer-Verlag, Berlin, 1995.
31. [P] N. PETERS, Turbulent Combustion, Cambridge University Press, 2000.
32. [R] J.-M. ROQUEJOFFRE, Eventual monotonicity and convergence to traveling fronts for the solutions of parabolic equations in cylinders, Annal. Inst. Poincaré, Analyse Nonlinéare 14 (1997), 499-552.
33. [V+] N. VLADIMIROVA, P. CONSTANTIN, A. KISELEV, O. RUCHAYSKIY AND L. RYZHIK, Flame enhancement and quenching in fluid flows, Combust. Theory Model. 7 (2003), 487-508.
34. [VoV] V.A. VOLPERT, A.I. VOLPERT, Existence and stability of multidimensional travelling waves in the monostable case, Israel Jour. Math. 110 (1999), 269-292.
35. [X1] J. XIN, Existence of planar flame fronts in convective-diflusive periodic media, Arch. Rat. Mech. Anal. 121 (1992), 205-233.
36. [X2] J. XIN, Existence and nonexistence of travelling waves and reaction-diffusion front propagation in periodic media, Jour. Stat. Phys. 73 (1993), 893-926.
37. [X3] J. XIN, Analysis and modelling of front propagation in heterogeneous media, SIAM Rev. 42 (2000), 161-230.
38. [X4] J. XIN, KPP front speeds in random shears and the parabolic Anderson model, Meth. Appl. Anal. 10 (2003), 191-198.