no. 3
Asymptotic Spreading of KPP Reactive Fronts in Incompressible Space-Time Random Flows
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 3, pp. 815-839. 
@article{AIHPC_2009__26_3_815_0,
     author = {Nolen, James and Xin, Jack},
     title = {Asymptotic {Spreading} of {KPP} {Reactive} {Fronts} in {Incompressible} {Space-Time} {Random} {Flows}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {815--839},
     publisher = {Elsevier},
     volume = {26},
     number = {3},
     year = {2009},
     doi = {10.1016/j.anihpc.2008.02.005},
     mrnumber = {2526403},
     zbl = {1177.35172},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2008.02.005/}
}
TY  - JOUR
AU  - Nolen, James
AU  - Xin, Jack
TI  - Asymptotic Spreading of KPP Reactive Fronts in Incompressible Space-Time Random Flows
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
SP  - 815
EP  - 839
VL  - 26
IS  - 3
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2008.02.005/
DO  - 10.1016/j.anihpc.2008.02.005
LA  - en
ID  - AIHPC_2009__26_3_815_0
ER  - 
%0 Journal Article
%A Nolen, James
%A Xin, Jack
%T Asymptotic Spreading of KPP Reactive Fronts in Incompressible Space-Time Random Flows
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 815-839
%V 26
%N 3
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2008.02.005/
%R 10.1016/j.anihpc.2008.02.005
%G en
%F AIHPC_2009__26_3_815_0
Nolen, James; Xin, Jack. Asymptotic Spreading of KPP Reactive Fronts in Incompressible Space-Time Random Flows. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 3, pp. 815-839. doi : 10.1016/j.anihpc.2008.02.005. http://www.numdam.org/articles/10.1016/j.anihpc.2008.02.005/

[1] Akcoglu M. A., Krengel U., Ergodic Theorems for Superadditive Processes, J. Reine Angew. Math. 323 (1981) 53-67. | MR | Zbl

[2] Ashurst W., Flow-Frequency Effect Upon Huygens Front Propagation, Combust. Theory Model. 4 (2000) 99-105. | Zbl

[3] Berestycki H., Hamel F., Front Propagation in Periodic Excitable Media, Comm. Pure Appl. Math. 60 (2002) 949-1032. | MR | Zbl

[4] Berestycki H., Nirenberg L., Travelling Fronts in Cylinders, Ann. Inst. H. Poincaré Anal. Non Linéaire 9 (1992) 497-572. | Numdam | MR | Zbl

[5] Cencini M., Torcini A., Vergni D., Vulpiani A., Thin Front Propagation in Steady and Unsteady Cellular Flows, Phys. Fluids 15 (3) (2003) 679-688. | MR

[6] Clavin P., Williams F. A., Theory of Premixed-Flame Propagation in Large-Scale Turbulence, J. Fluid Mech. 90 (1979) 598-604. | Zbl

[7] Chertkov M., Yakhot V., Hyugens Front Propagation in Turbulent Fluids, Phys. Rev. Lett. 80 (1998) 2837.

[8] Constantin P., Kiselev A., Oberman A., Ryzhik L., Bulk Burning Rate in Passive-Reactive Diffusion, Arch. Rat. Mech. Anal. 154 (2000) 53-91. | MR | Zbl

[9] Denet B., Possible Role of Temporal Correlations in the Bending of Turbulent Flame Velocity, Combust. Theory Model. 3 (1999) 585-589. | Zbl

[10] Freidlin M., Functional Integration and Partial Differential Equations, Ann. of Math. Stud., vol. 109, Princeton University Press, Princeton, NJ, 1985. | MR | Zbl

[11] Freidlin M., Sowers R., A Comparison of Homogenization and Large Deviations, With Applications to Wavefront Propagation, Stochastic Procsess. Appl. 82 (1999) 23-52. | MR | Zbl

[12] Gärtner J., Freidlin M. I., The Propagation of Concentration Waves in Periodic and Random Media, Dokl. Acad. Nauk SSSR 249 (1979) 521-525. | MR | Zbl

[13] Heinze S., Papanicolaou G., Stevens A., Variational Principles for Propagation Speeds in Inhomogeneous Media, SIAM J. Appl. Math 62 (1) (2001) 129-148. | MR | Zbl

[14] Karatzas I., Shreve S., Brownian Motion and Stochastic Calculus, Springer-Verlag, New York, 1991. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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). | MR | Zbl

[19] Lions P.-L., Souganidis P. E., Homogenization of Viscous Hamilton-Jacobi Equations in Stationary Ergodic Media, Comm. Partial Differential Equations 30 (2005) 335-375. | MR | Zbl

[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. | MR | Zbl

[21] Majda A., Souganidis P. E., Large Scale Front  dynamics for Turbulent Reaction-Diffusion Equations With Separated Velocity Scales, Nonlinearity 7 (1994) 1-30. | MR | Zbl

[22] Nolen J., Xin J., Reaction Diffusion Front Speeds in Spatially-Temporally Periodic Shear Flows, SIAM J. Multiscale Modeling and Simulation 1 (4) (2003) 554-570. | MR | Zbl

[23] Nolen J., Xin J., Min-Max Variational Principle and Front Speeds in Random Shear Flows, Methods Appl. Anal. 11 (4) (2004) 635-644. | MR | Zbl

[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. | MR | Zbl

[25] J. Nolen, J. Xin, Computing front speeds in randomly perturbed cellular flows by variational principle, Physica D (2008), in press.

[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. | MR | Zbl

[27] Peters N., Turbulent Combustion, Cambridge University Press, 2000. | MR | Zbl

[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] Souganidis P. E., Stochastic Homogenization of Hamilton-Jacobi Equations and Some Applications, Asymptotic Anal. 20 (1) (1999) 1-11. | MR | Zbl

[30] Varadhan S. R.S., Asymptotic Probabilities and Differential Equations, Comm. Pure Appl. Math. 19 (1966) 261-286. | MR | Zbl

[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. | MR | Zbl

[32] Xin J., Front Propagation in Heterogeneous Media, SIAM Rev. 42 (2) (June 2000) 161-230. | MR | Zbl

[33] Xin J., KPP Front Speeds in Random Shears and the Parabolic Anderson Problem, Methods Appl. Anal. 10 (2) (2003) 191-198. | MR | Zbl

[34] Yakhot V., Propagation Velocity of Premixed Turbulent Flames, Combust. Sci. Tech. 60 (1988) 191.

[35] A. Zlatoš, Pulsating front speed-up and quenching of reaction by fast advection, Preprint, 2007. | MR | Zbl

Cité par Sources :