Boundary layers and KPP fronts in a cellular flow

Archive for Rational Mechanics and Analysis

Volumn 184, Issue 1, 2007, Pages 23-48

  Novikov, Alexei ^a   Ryzhik, Lenya ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33847266469     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-006-0038-0     Document Type: Article

References (24)

1. ABEL, M., CELANI, A., VERGNI, D., VULPIANI, A.: Front propagation in laminar flows. Phys. Rev. E (3) 64, 046307-043620 (2001)
2. ABEL, M., CENCINI, M., VERGNI, D., VULPIANI, A.: Front speed enhancement in cellular flows. Chaos 12, 481-488 (2003)
3. AUDOLY, B., BERESTYCKI, H., POMEAU, Y.: Réaction-diffusion en écoulement stationnaire rapide. C. R. Math. Acad. Sci. Paris 328 II, 255-262 (2000)
4. BERESTYCKI, H.: The influence of advection on the propagation of fronts in reaction-diffusion equations. Nonlinear PDEs in Condensed Matter and Reactive Flows, NATO Science Series C, 569 (BERESTYCKI, H., POMEAU, Y., Eds.), Kluwer, Doordrecht, 2003
5. BERESTYCKI, H., HAMEL, F.: Front propagation in periodic excitable media. Comm. Pure Appl. Math. 55, 949-1032 (2002)
6. BERESTYCKI, H., HAMEL, F., NADIRASHVILI, N.: The speed of propagation for KPP type problems, I - Periodic framework. Jour. Eur. Math. Soc. (JEMS) 7, 173-213 (2005)
7. BERESTYCKI, H., HAMEL, F., NADIRASHVILI, N.: Elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena. Comm. Math. Phys. 253, 451-480 (2005)
8. CONSTANTIN, P., KISELEV, A., OBERMAN, A., RYZHIK, L.: Bulk burning rate in passive-reactive diffusion. Arch. Ration. Mech. Anal. 154, 53-91 (2001)
9. FANNJIANG, A., PAPANICOLAOU, G.: Convection enhanced diffusion for periodic flows. SIAM J. Appl. Math. 54, 333-408 (1994)
10. FREIDLIN, M., GÄRTNER, J.: On the propagation of concentration waves in periodic and random media. Soviet Math. Dokl. 20, 1282-1286 (1979)
11. FREIDLIN, M.: Reaction-diffusion in incompressible fluid: asymptotic problems. J. Differential Equations 179, 44-96 (2002)
12. FREIDLIN, M., WENTZELL, A.: Random perturbations of Hamiltonian systems. Memoir AMS, 1994
13. HEINZE, S.: Preprint, 2002
14. HEINZE, S.: Diffusion-Advection in Cellular Flows with Large Péclet Numbers. Arch. Ration. Mech. Anal. 168, 329-342 (2003)
15. HEINZE, S.: Large convection limits for KPP fronts, Preprint, 2005
16. HEINZE, S., PAPANICOLAOU, G., STEVENS, A.: Variational principles for propagation speeds in inhomogeneous media. SIAM J. Appl. Math. 62, 129-148 (2001)
17. KISELEV, A., RYZHIK, L.: Enhancement of the traveling front speeds in reaction-diffusion equations with advection. Ann. Inst. H Poincaré Anal Non Linéaire 18, 309-358 (2001)
18. KORALOV, L.: Random perturbations of two-dimensional Hamiltonian flows. Probab. Theory Related Fields 129, 37-62 (2004)
19. NOVIKOV, A., PAPANICOLAOU, G., RYZHIK, L.: Boundary layers for cellular flows at high Péclet numbers. Comm. Pure Appl. Math. 58, 867-922 (2005)
20. SOWERS, R.: A boundary layer theory for diffusively perturbed transport around a heteroclinic cycle. Comm. Pure Appl. Math. 58, 30-84 (2005)
21. VLADIMIROVA, N., CONSTANTIN, P., KISELEV, A., RUCHAYSKIY, O., RYZHIK, L.: Flame Enhancement and Quenching in Fluid Flows. Combust. Theory Model. 7, 487-508 (2003)
22. WEINBERGER, H.: On spreading speeds and traveling waves for growth and migration models in a periodic habitat. J. Math. Biol. 45, 511-548 (2002)
23. XIN, J.: Existence and nonexistenee of traveling waves and reaction-diffusion front propagation in periodic media. J. Stat. Phys. 73, 893-926 (1993)
24. XIN, J.: Analysis and modeling of front propagation in heterogeneous media. SIAM Rev. 42, 161-230 (2000)