Stability of travelling waves in a model for conical flames in two space dimensions

Annales Scientifiques de l'Ecole Normale Superieure

Volumn 37, Issue 3, 2004, Pages 469-506

  Hamel, François ^a   Monneau, Régis ^b   Roquejoffre, Jean Michel ^c  

^a CNRS   (France)

^b UNIVERSITÉ PARIS EST   (France)

^c INSTITUT UNIVERSITAIRE DE FRANCE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2942625416     PISSN: 00129593     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ansens.2004.03.001     Document Type: Article

References (41)

1. Agmon S. Nirenberg L. Properties of solutions of ordinary differential equations in Banach space Comm. Pure Appl. Math. 16 1963 121-239
2. Aronson D.G. Weinberger H.F. Nonlinear diffusion in population genetics, combustion and nerve propagation, in: Part. Diff. Eq. and Related Topics, in: Lecture Notes in Math. vol. 446 1975 5 49 Springer New York
3. Berestycki H. Hamel F. Front propagation in periodic excitable media Comm. Pure Appl. Math. 55 2002 949-1032
4. Berestycki H. Larrouturou B. Lions P.-L. Multidimensional travelling-wave solutions of a flame propagation model Arch. Rat. Mech. Anal. 111 1990 33-49
5. Berestycki H. Larrouturou B. Roquejoffre J.-M. Stability of travelling fronts in a curved flame model, Part I, Linear analysis Arch. Rat. Mech. Anal. 117 1992 97-117
6. Berestycki H. Nicolaenko B. Scheurer B. Traveling waves solutions to combustion models and their singular limits SIAM J. Math. Anal. 16 6 1985 1207-1242
7. Berestycki H. Nirenberg L. On the method of moving planes and the sliding method Bol. Soc. Bras. Mat. 22 1991 1-37
8. Berestycki H. Nirenberg L. Travelling fronts in cylinders Ann. Inst. H. Poincaré, Anal. Non Lin. 9 1992 497-572
9. Bonnet A. Hamel F. Existence of non-planar solutions of a simple model of premixed Bunsen flames SIAM J. Math. Anal. 31 1999 80-118
10. Bramson M. Convergence of Solutions of the Kolmogorov Equation to Travelling Waves Mem. Amer. Math. Soc. vol. 44 1983
11. Brazhnik P.K. Tyson J.J. On traveling wave solutions of Fisher's equation in two spatial dimensions SIAM J. Appl. Math. 60 2000 371-391
12. Buckmaster J.D. Ludford G.S.S. Lectures on Mathematical Combustion, in: CBMS-NSF Conf. Series in Applied Math. vol. 43 1983 SIAM
13. Caffarelli L.A. Cabré X. Fully Nonlinear Elliptic Equations, in: Colloquium Publications, in: Amer. Math. Soc. vol. 43 1995
14. Crandall M.G. Ishii H. Lions P.-L. User's guide to viscosity solutions of second order partial differential equations Bull. Amer. Math. Soc. (N.S.) 27 1992 1-67
15. Collet P. Eckmann J.-P. Space-time behaviour in problems of hydrodynamic type: a case study Nonlinearity 5 6 1992 1265-1302
16. Fife P.C. Dynamics of internal layers and diffusive interfaces, in: Cbms-Nsf Regional Conference, in: Series in Applied Mathematics vol. 53 1988
17. Fife P.C. McLeod J.B. The approach of solutions of non-linear diffusion equations to travelling front solutions Arch. Rat. Mech. Anal. 65 1977 335-361
18. Gilbarg D. Trudinger N.S. Elliptic Partial Differential Equations of Second Order 1997 Springer-Verlag
19. N with conical-shaped level sets Comm. Partial Differential Equations 25 2000 769-819
20. Hamel F. Monneau R. Existence and uniqueness for a free boundary problem arising in combustion theory Interfaces Free Boundaries 4 2002 167-210
21. N Arch. Ration. Mech. Anal. 157 2001 91-163
22. Henry D. Geometric Theory of Semilinear Parabolic Equations, in: Lecture Notes in Math. 1981 Springer Verlag New York
23. Ishii H. On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDE's Comm. Pure Appl. Math. 42 1989 15-45
24. Joulin G. Dynamique des fronts de flammes Modélisation de la combustion, Images des Mathématiques 1996 CNRS
25. Kanel' Ya.I. Certain problems of burning-theory equations Sov. Math. Dokl. 2 1961 48-51
26. Kanel' Ya.I. Stabilization of solution of the Cauchy problem for equations encountered in combustion theory Mat. Sbornik 59 1962 245-288
27. Levermore C.D. Xin J.X. Multidimensional stability of travelling waves in a bistable reaction-diffusion equation, II Comm. Partial Differential Equations 17 1992 1901-1924
28. Lewis B. Von Elbe G. Combustion, Flames and Explosions of Gases 1961 Academic Press New York
29. Mallordy J.-F. Roquejoffre J.-M. A parabolic equation of the KPP type in higher dimensions SIAM J. Math. Anal. 26 1995 1-20
30. Matkowsky B.J. Olagunju D.O. Pulsations in a burner-stabilized premixed plane flame SIAM J. Appl. Math. 40 1981 551-562
31. Michelson D. Stability of the Bunsen flame profiles in the Kuramoto-Sivashinsky equation SIAM J. Math. Anal. 27 1996 765-781
32. Ninomiya H. Taniguchi M. Stability of traveling curved fronts in a curvature flow with driving force, Meth. Appl. Anal., submitted for publication
33. Roquejoffre J.-M. Stability of travelling fronts in a curved flame model, Part II: Non-linear orbital stability Arch. Rat. Mech. Anal. 117 1992 119-153
34. Roquejoffre J.-M. Convergence to travelling waves for solutions of a class of semilinear parabolic equation J. Differential Equations 108 1994 262-295
35. Roquejoffre J.-M. Eventual monotonicity and convergence to travelling fronts for the solutions of parabolic equations in cylinders Ann. Inst. H. Poincaré, Anal. Non Lin. 14 1997 499-552
36. Sattinger D.H. Stability of waves of nonlinear parabolic systems Adv. Math. 22 1976 312-355
37. Sattinger D.H. Weighted norms for the stability of travelling waves J. Differential Equations 25 1977 130-144
38. Sivashinsky G.I. The structure of Bunsen flames J. Chem. Phys. 62 1975 638-643
39. Stewart H.B. Generation of analytic semigroups by strongly elliptic operators under general boundary conditions Trans. Amer. Math. Soc. 259 1980 299-310
40. Williams F. Combustion Theory 1983 Addison-Wesley Reading, MA
41. Xin J.X. Muldimensional stability of travelling waves in a bistable reaction-diffusion equation, I Comm. Partial Differential Equations 17 1992 1889-1899