Traveling waves with paraboloid like interfaces for balanced bistable dynamics
Xinfu Chen; Jong-Shenq Guo; François Hamel; Hirokazu Ninomiya; Jean-Michel Roquejoffre
Annales de l'I.H.P. Analyse non linéaire (2007)
- Volume: 24, Issue: 3, page 369-393
- ISSN: 0294-1449
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topChen, Xinfu, et al. "Traveling waves with paraboloid like interfaces for balanced bistable dynamics." Annales de l'I.H.P. Analyse non linéaire 24.3 (2007): 369-393. <http://eudml.org/doc/78740>.
@article{Chen2007,
author = {Chen, Xinfu, Guo, Jong-Shenq, Hamel, François, Ninomiya, Hirokazu, Roquejoffre, Jean-Michel},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {interface; level set},
language = {eng},
number = {3},
pages = {369-393},
publisher = {Elsevier},
title = {Traveling waves with paraboloid like interfaces for balanced bistable dynamics},
url = {http://eudml.org/doc/78740},
volume = {24},
year = {2007},
}
TY - JOUR
AU - Chen, Xinfu
AU - Guo, Jong-Shenq
AU - Hamel, François
AU - Ninomiya, Hirokazu
AU - Roquejoffre, Jean-Michel
TI - Traveling waves with paraboloid like interfaces for balanced bistable dynamics
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2007
PB - Elsevier
VL - 24
IS - 3
SP - 369
EP - 393
LA - eng
KW - interface; level set
UR - http://eudml.org/doc/78740
ER -
References
top- [1] Alberti G., Ambrosio L., Cabré X., On a long-standing conjecture of E. De Giorgi: old and recent results, Acta Appl. Math.65 (2001) 9-33. Zbl1121.35312MR1843784
- [2] Allen S., Cahn J.W., A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening, Acta. Metall.27 (1979) 1084-1095.
- [3] Ambrosio L., Cabré X., Entire solutions of semilinear elliptic equations in and a conjecture of De Giorgi, J. Amer. Math. Soc.13 (2000) 725-739. Zbl0968.35041MR1775735
- [4] Aronson D.G., Weinberger H.F., Multidimensional nonlinear diffusions arising in population genetics, Adv. Math.30 (1978) 33-76. Zbl0407.92014MR511740
- [5] Berestycki H., Caffarelli L., Nirenberg L., Monotonicity for elliptic equations in unbounded Lipschitz domains, Comm. Pure Appl. Math.50 (1997) 1089-1111. Zbl0906.35035MR1470317
- [6] Berestycki H., Hamel F., Monneau R., One-dimensional symmetry of bounded entire solutions of some elliptic equations, Duke Math. J.103 (2000) 375-396. Zbl0954.35056MR1763653
- [7] H. Berestycki, B. Larrouturou, Planar travelling front solutions of reaction–diffusion problems, preprint. Zbl0612.76079
- [8] Bonnet A., Hamel F., Existence of nonplanar solutions of a simple model of premixed Bunsen flames, SIAM J. Math. Anal.31 (1999) 80-118. Zbl0942.35072MR1742304
- [9] Caffarelli L.A., Cabré X., Fully Nonlinear Elliptic Equations, Colloquium Publications, vol. 43, Amer. Math. Soc., 1995. Zbl0834.35002MR1351007
- [10] Carr J., Pego R.L., Invariant manifolds for metastable patterns in , Proc. Roy. Soc. Edinburgh Sect. A116 (1990) 133-160. Zbl0738.35023MR1076358
- [11] Chen X., Generation and propagation of interfaces for reaction–diffusion equations, J. Differential Equations96 (1992) 116-141. Zbl0765.35024
- [12] Chen X., Spectrum for the Allen–Cahn, Cahn–Hilliard, and phase-field equations for generic interfaces, Comm. Partial Differential Equations19 (1994) 1371-1395. Zbl0811.35098
- [13] Chen X., Generation, propagation, and annihilation of metastable patterns, J. Differential Equations206 (2004) 399-437. Zbl1061.35014MR2095820
- [14] X. Chen, J.-S. Guo, H. Ninomiya, Entire solutions of reaction–diffusion equations with balanced bistable nonlinearities, Proc. Roy. Soc. Edinburgh Sect. A, in press. Zbl1123.35024
- [15] Chen X., Taniguchi M., Instability of spherical interfaces in a nonlinear free boundary problem, Adv. Differential Equations5 (2000) 747-772. Zbl1012.35081MR1750117
- [16] De Giorgi E., Convergence problems for functionals and operators, in: Proc. Int. Meeting on Recent Methods in Nonlinear Analysis, Rome, 1978, Pitagora, 1979, pp. 131-188. Zbl0405.49001MR533166
- [17] De Mottoni P., Schatzman M., Development of interfaces in , Proc. Roy. Soc. Edinburgh Sect. A116 (1990) 207-220. Zbl0725.35009MR1084732
- [18] Ei S.-I., The motion of weakly interaction pulses in reaction–diffusion systems, J. Dynamics Differential Equations14 (2002) 85-137. Zbl1007.35039
- [19] Evans L.C., Soner H.M., Souganidis P.E., Phase transitions and generalized motion by mean curvature, Comm. Pure Appl. Math.45 (1992) 1097-1123. Zbl0801.35045MR1177477
- [20] Fife P.C., Dynamics of Internal Layers and Diffusive Interfaces, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 53, 1988. Zbl0684.35001MR981594
- [21] Fife P.C., McLeod J.B., The approach of solutions of non-linear diffusion equations to traveling front solutions, Arch. Rational Mech. Anal.65 (1977) 335-361. Zbl0361.35035MR442480
- [22] Fusco G., A geometric approach to the dynamics of for smallε, in: Kirchgassner (Ed.), Lecture Notes in Physics, vol. 359, 1990, pp. 53-73. Zbl0715.35038
- [23] Fusco G., Hale J.K., Slow-motion manifolds, dormant instability, and singular perturbations, J. Dynamics Differential Equations1 (1989) 75-94. Zbl0684.34055MR1010961
- [24] Ghoussoub N., Gui C., On a conjecture of De Giorgi and some related problems, Math. Ann.311 (1998) 481-491. Zbl0918.35046MR1637919
- [25] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1997. Zbl0562.35001
- [26] Hamel F., Monneau R., Solutions of semilinear elliptic equations in with conical-shaped level sets, Comm. Partial Differential Equations25 (2000) 769-819. Zbl0952.35041MR1759793
- [27] Hamel F., Monneau R., Existence and uniqueness for a free boundary problem arising in combustion theory, Interfaces Free Boundaries4 (2002) 167-210. Zbl1078.80004MR1950528
- [28] Hamel F., Monneau R., Roquejoffre J.-M., Stability of traveling waves in a model for conical flames in two space dimensions, Ann. Sci. École Norm. Sup.37 (2004) 469-506. Zbl1085.35075MR2060484
- [29] Hamel F., Monneau R., Roquejoffre J.-M., Existence and qualitative properties of multidimensional conical bistable fronts, Disc. Cont. Dyn. Systems13 (2005) 1069-1096. Zbl1097.35078MR2166719
- [30] Hamel F., Monneau R., Roquejoffre J.-M., Asymptotic properties and classification of bistable fronts with Lipschitz level sets, Disc. Cont. Dyn. Systems14 (2006) 75-92. Zbl1194.35151MR2170314
- [31] Hamel F., Nadirashvili N., Travelling waves and entire solutions of the Fisher-KPP equation in , Arch. Rational Mech. Anal.157 (2001) 91-163. Zbl0987.35072MR1830037
- [32] Haragus M., Scheel A., Corner defects in almost planar interface propagation, Ann. Inst. H. Poincaré Anal. Non Linéaire23 (2006) 283-329. Zbl1098.35085MR2217654
- [33] Ilmanen T., Convergence of the Allen–Cahn equation to Brakke's motion, J. Differential Geom.38 (1993) 417-461. Zbl0784.53035
- [34] Ninomiya H., Taniguchi M., Traveling curved fronts of a mean curvature flow with constant driving force, in: Free Boundary Problems: Theory and Applications, I, GAKUTO Internat. Ser. Math. Sci. Appl., vol. 13, 2000, pp. 206-221. Zbl0957.35124MR1793036
- [35] Ninomiya H., Taniguchi M., Stability of traveling curved fronts in a curvature flow with driving force, Methods Appl. Anal.8 (2001) 429-450. Zbl1007.35004MR1904754
- [36] Ninomiya H., Taniguchi M., Existence and global stability of traveling curved fronts in the Allen–Cahn equations, J. Differential Equations213 (2005) 204-233. Zbl1159.35378
- [37] H. Ninomiya, M. Taniguchi, Global stability of traveling curved fronts in the Allen–Cahn equations, Disc. Cont. Dyn. Systems, submitted for publication. Zbl1118.35012
- [38] Ouyang T., Shi J., Exact multiplicity of positive solutions for a class of semilinear problems, J. Differential Equations146 (1998) 121-156. Zbl0918.35049MR1625731
- [39] O. Savin, Phase transitions: regularity of flat level sets, preprint. Zbl1180.35499
- [40] Soner H.M., Motion of a set by the curvature of its boundary, J. Differential Equations101 (1993) 313-372. Zbl0769.35070MR1204331
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