Asymptotic spreading of KPP reactive fronts in incompressible space-time random flows

 Access to full text

 Full (PDF)

1. [1] Akcoglu M.A., Krengel U., Ergodic theorems for superadditive processes, J. Reine Angew. Math.323 (1981) 53-67. Zbl0453.60039MR611442
2. [2] Ashurst W., Flow-frequency effect upon Huygens front propagation, Combust. Theory Model.4 (2000) 99-105. Zbl0948.76630
3. [3] Berestycki H., Hamel F., Front propagation in periodic excitable media, Comm. Pure Appl. Math.60 (2002) 949-1032. Zbl1024.37054MR1900178
4. [4] Berestycki H., Nirenberg L., Travelling fronts in cylinders, Ann. Inst. H. Poincaré Anal. Non Linéaire9 (1992) 497-572. Zbl0799.35073MR1191008
5. [5] Cencini M., Torcini A., Vergni D., Vulpiani A., Thin front propagation in steady and unsteady cellular flows, Phys. Fluids15 (3) (2003) 679-688. Zbl1185.76077MR1958079
6. [6] Clavin P., Williams F.A., Theory of premixed-flame propagation in large-scale turbulence, J. Fluid Mech.90 (1979) 598-604. Zbl0434.76052
7. [7] Chertkov M., Yakhot V., Hyugens front propagation in turbulent fluids, Phys. Rev. Lett.80 (1998) 2837. 
8. [8] Constantin P., Kiselev A., Oberman A., Ryzhik L., Bulk burning rate in passive-reactive diffusion, Arch. Rat. Mech. Anal.154 (2000) 53-91. Zbl0979.76093MR1778121
9. [9] Denet B., Possible role of temporal correlations in the bending of turbulent flame velocity, Combust. Theory Model.3 (1999) 585-589. Zbl0948.76086
10. [10] Freidlin M., Functional Integration and Partial Differential Equations, Ann. of Math. Stud., vol. 109, Princeton University Press, Princeton, NJ, 1985. Zbl0568.60057MR833742
11. [11] Freidlin M., Sowers R., A comparison of homogenization and large deviations, with applications to wavefront propagation, Stochastic Procsess. Appl.82 (1999) 23-52. Zbl0996.60035MR1695068
12. [12] Gärtner J., Freidlin M.I., The propagation of concentration waves in periodic and random media, Dokl. Acad. Nauk SSSR249 (1979) 521-525. Zbl0447.60060MR553200
13. [13] Heinze S., Papanicolaou G., Stevens A., Variational principles for propagation speeds in inhomogeneous media, SIAM J. Appl. Math62 (1) (2001) 129-148. Zbl0995.35031MR1857539
14. [14] Karatzas I., Shreve S., Brownian Motion and Stochastic Calculus, Springer-Verlag, New York, 1991. Zbl0734.60060MR1121940
15. [15] Khouider B., Bourlioux A., Majda A., Parameterizing turbulent flame speed – Part I: unsteady shears, flame residence time and bending, Combust. Theory Model.5 (2001) 295-318. Zbl1114.80303MR1860152
16. [16] Kosygina E., Rezakhanlou F., Varadhan S.R.S., Stochastic homogenization of Hamilton–Jacobi–Bellman equations, Comm. Pure Appl. Math.59 (10) (2006) 1489-1521. Zbl1111.60055MR2248897
17. [17] E. Kosygina, S.R.S. Varadhan, Homogenization of Hamilton–Jacobi–Bellman equations with respect to time–space shifts in a stationary ergodic medium, Preprint, 2006. Zbl1144.35008MR2400607
18. [18] Krylov N.V., Safonov M.V., A property of the solutions of parabolic equations with measurable coefficients, Izv. Akad. Nauk SSSR Ser. Mat.16 (1) (1981) 151-164, (English translation). Zbl0464.35035MR563790
19. [19] Lions P.-L., Souganidis P.E., Homogenization of viscous Hamilton–Jacobi equations in stationary ergodic media, Comm. Partial Differential Equations30 (2005) 335-375. Zbl1065.35047MR2131058
20. [20] Majda A., Souganidis P.E., Flame fronts in a turbulent combustion model with fractal velocity fields, Comm. Pure Appl. Math. LI (1998) 1337-1348. Zbl0939.35097MR1639220
21. [21] Majda A., Souganidis P.E., Large scale front  dynamics for turbulent reaction–diffusion equations with separated velocity scales, Nonlinearity7 (1994) 1-30. Zbl0839.76093MR1260130
22. [22] Nolen J., Xin J., Reaction diffusion front speeds in spatially-temporally periodic shear flows, SIAM J. Multiscale Modeling and Simulation1 (4) (2003) 554-570. Zbl1053.35068MR2029591
23. [23] Nolen J., Xin J., Min-max variational principle and front speeds in random shear flows, Methods Appl. Anal.11 (4) (2004) 635-644. Zbl1107.35366MR2195373
24. [24] Nolen J., Xin J., Variational principle of KPP front speeds in temporally random shear flows with applications, Commun. Math. Phys.269 (2007) 493-532. Zbl1114.35095MR2274555
25. [25] J. Nolen, J. Xin, Computing front speeds in randomly perturbed cellular flows by variational principle, Physica D (2008), in press. Zbl1155.76061
26. [26] Novikov A., Ryzhik L., Bounds on the speed of propagation of the KPP fronts in a cellular flow, Arch. Rat. Mech. Anal.184 (2007) 23-48. Zbl1109.76064MR2289862
27. [27] Peters N., Turbulent Combustion, Cambridge University Press, 2000. Zbl0955.76002MR1792350
28. [28] Ronney P., Some open issues in premixed turbulent combustion, in: Buckmaster J.D., Takeno T. (Eds.), Modeling in Combustion Science, Lecture Notes in Physics, vol. 449, Springer-Verlag, Berlin, 1995, pp. 3-22. 
29. [29] Souganidis P.E., Stochastic homogenization of Hamilton–Jacobi equations and some applications, Asymptotic Anal.20 (1) (1999) 1-11. Zbl0935.35008MR1697831
30. [30] Varadhan S.R.S., Asymptotic probabilities and differential equations, Comm. Pure Appl. Math.19 (1966) 261-286. Zbl0147.15503MR203230
31. [31] Vladimirova N., Constantin P., Kiselev A., Ruchayskiy O., Ryzhik L., Flame enhancement and quenching in fluid flows, Combust. Theory Model.7 (2003) 487-508. Zbl1068.76570MR2007570
32. [32] Xin J., Front propagation in heterogeneous media, SIAM Rev.42 (2) (June 2000) 161-230. Zbl0951.35060MR1778352
33. [33] Xin J., KPP front speeds in random shears and the parabolic Anderson problem, Methods Appl. Anal.10 (2) (2003) 191-198. Zbl1052.35099MR2074747
34. [34] Yakhot V., Propagation velocity of premixed turbulent flames, Combust. Sci. Tech.60 (1988) 191. 
35. [35] A. Zlatoš, Pulsating front speed-up and quenching of reaction by fast advection, Preprint, 2007. Zbl1149.35308MR2368331

1. James Nolen, Lenya Ryzhik, Traveling waves in a one-dimensional heterogeneous medium