Travelling waves in two-dimensional reactive Boussinesq systems with no-slip boundary conditions

Nonlinearity

Volumn 19, Issue 11, 2006, Pages

  Constantin, Peter ^a   Lewicka, Marta ^b   Ryzhik, Lenya ^a  

^a UNIVERSITY OF CHICAGO   (United States)

^b University of Minnesota   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846103881     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/19/11/006     Document Type: Review

References (17)

1. Adams R A 1975 Sobolev Spaces (Pure and Applied Mathematics vol 65) (New York: Academic)
2. Agmon S, Douglis A and Nirenberg L 1964 Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II Commun. Pure Appl. Math. 17 35-92
3. Belk M, Kazmierczak B and Volpert V 2005 Existence of reaction-diffusion-convection waves in unbounded strips Int. J. Math. Math. Sci. 2 169-93
4. Berestycki H 2003 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 vol 569) ed H Berestycki and Y Pomeau (Doordrecht: Kluwer)
5. Berestycki H, Constantin P and Ryzhik L 2006 Non-planar fronts in Boussinesq reactive flows Ann. Inst. Henri Poincare 23 407-37
6. Berestycki H and Larrouturou B 1989 A semi-linear elliptic equation in a strip arising in a two-dimensional flame propagation model J. Reine Angew. Math. 396 14-40
7. Berestycki H, Larrouturou B and Lions P L 1990 Multi-dimensional traveling wave solutions of a flame propagation model Arch. Ration. Mech. Anal. 111 33-49
8. Berestycki H, Nicolaenco B and Scheurer B 1983 Traveling wave solutions to combustion models and their singular limits SIAM J. Math. Anal. 16 1207-42
9. Constantin P, Kiselev A and Ryzhik L 2003 Fronts in reactive convection: bounds, stability and instability Commun. Pure Appl. Math. 56 1781-803
10. Ducrot A, Marion M and Volpert V 2006 Reaction-diffusion-convection problems with non Fredholm operators Int. J. Pure Appl. Math. 27 179-204
11. Galdi G P 1998 An introduction to the mathematical theory of the Navier-Stokes equations Springer Tracts in Natural Philosophy 38 vol 38 (Berlin: Springer) 39
12. Gilbarg D and Trudinger N 2001 Elliptic Partial Differential Equations Of Second Order (Berlin: Springer)
13. Roquejoffre J M 1997 Eventual monotonicity and convergence to traveling fronts for the solutions of parabolic equations in cylinders Ann. Inst. Henri Poincare 14 499-552
14. Texier-Picard R and Volpert V 2001 Problemes de reaction-diffusion- convection dans des cylindres non bornes C. R. Acad. Sci. Paris Ser. I 333 1077-82
15. Texier-Picard R and Volpert V 2003 Reaction-diffusion-convection problems in unbounded cylinders Rev. Mat. Complut. 16 233-76
16. Vladimirova N and Rosner R 2003 Model flames in the Boussinesq limit: the effects of feedback Phys. Rev. E 67 066305
17. Xin J 2000 Front propagation in heterogeneous media SIAM Rev. 42 161-230