Comptes Rendus
Partial Differential Equations
Fronts and invasions in general domains
Comptes Rendus. Mathématique, Volume 343 (2006) no. 11-12, pp. 711-716.

This Note defines generalized waves and fronts for reaction–diffusion equations in general domains. Some qualitative monotonicity and uniqueness results are given for invasion and almost-planar fronts.

Cette Note définit des notions générales d'ondes et fronts pour des équations de réaction–diffusion dans des domaines quelconques et donne des résultats qualitatifs de monotonie et d'unicité pour des fronts d'invasion ou presque plans.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2006.09.036
Henri Berestycki 1; François Hamel 2

1 EHESS, CAMS, 54, boulevard Raspail, 75006 Paris, France
2 Université Aix-Marseille III, LATP, avenue Escadrille Normandie-Niemen, 13397 Marseille cedex 20, France
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Henri Berestycki; François Hamel. Fronts and invasions in general domains. Comptes Rendus. Mathématique, Volume 343 (2006) no. 11-12, pp. 711-716. doi : 10.1016/j.crma.2006.09.036. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.09.036/

[1] H. Berestycki; F. Hamel Front propagation in periodic excitable media, Comm. Pure Appl. Math., Volume 55 (2002), pp. 949-1032

[2] H. Berestycki, F. Hamel, Generalized travelling waves for reaction–diffusion equations, in press

[3] H. Berestycki, F. Hamel, On a general definition of travelling waves and their properties, preprint

[4] H. Berestycki, F. Hamel, Reaction–Diffusion Equations and Propagation Phenomena, Springer, 2007, in press

[5] H. Berestycki, F. Hamel, H. Matano, Travelling waves in the presence of an obstacle, preprint

[6] H. Berestycki; F. Hamel; N. Nadirashvili The speed of propagation for KPP type problems. I – Periodic framework, J. Eur. Math. Soc., Volume 7 (2005), pp. 173-213

[7] A. Bonnet; F. Hamel Existence of non-planar solutions of a simple model of premixed Bunsen flames, SIAM J. Math. Anal., Volume 31 (1999), pp. 80-118

[8] P.C. Fife Mathematical Aspects of Reacting and Diffusing Systems, Springer-Verlag, 1979

[9] F. Hamel; R. Monneau; J.-M. Roquejoffre Existence and qualitative properties of conical bistable fronts, Disc. Cont. Dyn. Systems, Volume 13 (2005), pp. 1069-1096

[10] F. Hamel; N. Nadirashvili Travelling waves and entire solutions of the Fisher-KPP equation in RN, Arch. Ration. Mech. Anal., Volume 157 (2001), pp. 91-163

[11] M. Haragus; A. Scheel Corner defects in almost planar interface propagation, Ann. Inst. H. Poincaré Anal. Non Linéaire, Volume 23 (2006), pp. 283-329

[12] H. Matano, Oral communication

[13] H. Ninomiya; M. Taniguchi Existence and global stability of traveling curved fronts in the Allen–Cahn equations, J. Differential Equations, Volume 213 (2005), pp. 204-233

[14] N. Shigesada; K. Kawasaki Biological Invasions: Theory and Practice, Oxford University Press, Oxford, 1997

[15] X. Xin Existence of planar flame fronts in convective-diffusive periodic media, Arch. Ration. Mech. Anal., Volume 121 (1992), pp. 205-233

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