@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://archive.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://archive.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://archive.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://archive.numdam.org/articles/10.1016/j.anihpc.2008.02.005/
[1] Ergodic Theorems for Superadditive Processes, J. Reine Angew. Math. 323 (1981) 53-67. | MR | Zbl
, ,[2] Flow-Frequency Effect Upon Huygens Front Propagation, Combust. Theory Model. 4 (2000) 99-105. | Zbl
,[3] Front Propagation in Periodic Excitable Media, Comm. Pure Appl. Math. 60 (2002) 949-1032. | MR | Zbl
, ,[4] Travelling Fronts in Cylinders, Ann. Inst. H. Poincaré Anal. Non Linéaire 9 (1992) 497-572. | Numdam | MR | Zbl
, ,[5] Thin Front Propagation in Steady and Unsteady Cellular Flows, Phys. Fluids 15 (3) (2003) 679-688. | MR
, , , ,[6] Theory of Premixed-Flame Propagation in Large-Scale Turbulence, J. Fluid Mech. 90 (1979) 598-604. | Zbl
, ,[7] Hyugens Front Propagation in Turbulent Fluids, Phys. Rev. Lett. 80 (1998) 2837.
, ,[8] Bulk Burning Rate in Passive-Reactive Diffusion, Arch. Rat. Mech. Anal. 154 (2000) 53-91. | MR | Zbl
, , , ,[9] Possible Role of Temporal Correlations in the Bending of Turbulent Flame Velocity, Combust. Theory Model. 3 (1999) 585-589. | Zbl
,[10] Functional Integration and Partial Differential Equations, Ann. of Math. Stud., vol. 109, Princeton University Press, Princeton, NJ, 1985. | MR | Zbl
,[11] A Comparison of Homogenization and Large Deviations, With Applications to Wavefront Propagation, Stochastic Procsess. Appl. 82 (1999) 23-52. | MR | Zbl
, ,[12] The Propagation of Concentration Waves in Periodic and Random Media, Dokl. Acad. Nauk SSSR 249 (1979) 521-525. | MR | Zbl
, ,[13] Variational Principles for Propagation Speeds in Inhomogeneous Media, SIAM J. Appl. Math 62 (1) (2001) 129-148. | MR | Zbl
, , ,[14] Brownian Motion and Stochastic Calculus, Springer-Verlag, New York, 1991. | MR | Zbl
, ,[15] Parameterizing Turbulent Flame Speed - Part I: Unsteady Shears, Flame Residence Time and Bending, Combust. Theory Model. 5 (2001) 295-318. | MR | Zbl
, , ,[16] 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] 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] Homogenization of Viscous Hamilton-Jacobi Equations in Stationary Ergodic Media, Comm. Partial Differential Equations 30 (2005) 335-375. | MR | Zbl
, ,[20] Flame Fronts in a Turbulent Combustion Model With Fractal Velocity Fields, Comm. Pure Appl. Math. LI (1998) 1337-1348. | MR | Zbl
, ,[21] Large Scale Front dynamics for Turbulent Reaction-Diffusion Equations With Separated Velocity Scales, Nonlinearity 7 (1994) 1-30. | MR | Zbl
, ,[22] Reaction Diffusion Front Speeds in Spatially-Temporally Periodic Shear Flows, SIAM J. Multiscale Modeling and Simulation 1 (4) (2003) 554-570. | MR | Zbl
, ,[23] Min-Max Variational Principle and Front Speeds in Random Shear Flows, Methods Appl. Anal. 11 (4) (2004) 635-644. | MR | Zbl
, ,[24] 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] 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] Turbulent Combustion, Cambridge University Press, 2000. | MR | Zbl
,[28] Some Open Issues in Premixed Turbulent Combustion, in: , (Eds.), Modeling in Combustion Science, Lecture Notes in Physics, vol. 449, Springer-Verlag, Berlin, 1995, pp. 3-22.
,[29] Stochastic Homogenization of Hamilton-Jacobi Equations and Some Applications, Asymptotic Anal. 20 (1) (1999) 1-11. | MR | Zbl
,[30] Asymptotic Probabilities and Differential Equations, Comm. Pure Appl. Math. 19 (1966) 261-286. | MR | Zbl
,[31] Flame Enhancement and Quenching in Fluid Flows, Combust. Theory Model. 7 (2003) 487-508. | MR | Zbl
, , , , ,[32] Front Propagation in Heterogeneous Media, SIAM Rev. 42 (2) (June 2000) 161-230. | MR | Zbl
,[33] KPP Front Speeds in Random Shears and the Parabolic Anderson Problem, Methods Appl. Anal. 10 (2) (2003) 191-198. | MR | Zbl
,[34] 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
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