Existence and qualitative properties of multidimensional conical bistable fronts

Discrete and Continuous Dynamical Systems

Volumn 13, Issue 4, 2005, Pages 1069-1096

  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

Bistable elliptic equations; Conical travelling fronts

Indexed keywords

EID: 28444489648     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2005.13.1069     Document Type: Article

References (27)

1. 3 and a conjecture of De Giorgi; J. Amer. Math. Soc. 13 (2000), pp. 725-739
2. G. BARLES, H.M. SONER, P.E SOUGANIDIS Front propagation and phase field theory, SIAM J. Control Optim. 31 (1993), pp. 439-469.
3. H. BERESTYCKI, L.A. CAFFARELLI, L. NIRENBERG, Further qualitative properties for elliptic equations in unbounded domains, Dedicated to Ennio De Giorgi. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 25 (1998), pp. 69-94.
4. H. BERESTYCKI, F. HAMEL, R. MONNEAU, One-dimensional symmetry of bounded entire solutions of some elliptic equations, Duke Math. J. 103 (2000), pp. 375-396.
5. H. BERESTYCKI, B. NICOLAENKO, B. SCHEURER, Traveling waves solutions to combustion models and their singular limits, SIAM J. Math. Anal. 16, 6 (1985), pp 1207-1242.
6. H. BERESTYCKI, L. NIRENBERG, On the method of moving planes and the sliding method, Bol. Soc. Bras. Mat. 22 (1991), pp 1-37.
7. H. BERESTYCKI, L. NIRENBERG, Travelling fronts in cylinders, Ann. Inst. H. Poincaré, Anal. Non Lin. 9 (1992), pp 497-572.
8. X. CABRÉ, F. HAMEL, R. MONNEAU, J.-M. ROQUEJOFFRE, Multidimensional bistable reaction-diffusion fronts with vertical asymptotic directions, in preparation.
9. L.A. CAFFARELLI, X. CABRÉ, Fully Nonlinear Elliptic Equations, Colloquium Publications, Amer. Math. Soc. 43, 1995.
10. M.G. CRANDALL, H. ISHII, P.-L. LIONS, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.) 27 (1992), pp 1-67.
11. L.C. EVANS, J. SPRUCK, Motion of level sets by mean curvature I, J. Differential Geom. 33 (1991), pp. 635-681,
12. II. Trans. Amer. Math. Soc. 330 (1992), pp. 321-332,
13. III. J. Geom. Anal. 2 (1992), pp. 121-150.
14. P.C. FIFE, Dynamics of internal layers and diffusive interfaces, Cbms-Nsf Regional Conference, Series in Applied Mathematics 53, 1988.
15. P.C. FIFE, J.B. MCLEOD, The approach of solutions of non-linear diffusion equations to travelling front solutions, Arch. Rat. Mech. Anal. 65 (1977), pp 335-361.
16. N. GHOUSSOUB, C. GUI, On De Giorgi's conjecture in dimensions 4 and 5, Ann. of Math. 157 (2003), pp. 313-334.
17. N with conical-shaped level sets, Comm. Part. Diff. Eq. 25 (2000), pp 769-819.
18. F. HAMEL, R. MONNEAU, Existence and uniqueness for a free boundary problem arising in combustion theory, Interfaces Free Boundaries 4 (2002), pp 167-210.
19. F. HAMEL, R. MONNEAU, J.-M. ROQUEJOFFRE, Stability of travelling waves in a model for conical flames in two space dimensions, Ann. Scient. Ec. Norm. Sup., 37 (2004), pp. 469-506.
20. F. HAMEL, R. MONNEAU, J.-M. ROQUEJOFFRE, Asymptotic properties and classification of bistable fronts with Lipschitz level sets, preprint.
21. N, Arch. Ration. Mech. Anal. 157 (2001), pp 91-163.
22. M. HARAGUS, A. SCHEEL, Corner defects in almost planar interface propagation, online preprint http://www.math.umn.edu/ scheel/publications.html.
23. D. HENRY, Geometric theory of semilinear parabolic equations, Lectures Notes in Math., Springer Verlag, New York, 1981.
24. H. ISHII, On uniqueness and existence of viscosity solutions of Fully nonlinear second-order elliptic PDE's, Comm. Pure Appl. Math. 42 (1989), pp 15-45.
25. H. NINOMIYA, M. TANIGUCHI, Existence and global stability of travelling curved fronts in the Allen-Cahn equations, to appear in J. Diff. Eq.
26. O. SAVIN, Phase transitions: regularity of flat level sets; Preprint.
27. D.H. SATTINGER, Stability of waves of nonlinear parabolic systems, Adv. Math. 22 (1976), pp 312-355.