[Fronts et invasions dans des domaines quelconques]
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.
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.
Accepté le :
Publié le :
Henri Berestycki 1 ; François Hamel 2
@article{CRMATH_2006__343_11-12_711_0,
author = {Henri Berestycki and Fran\c{c}ois Hamel},
title = {Fronts and invasions in general domains},
journal = {Comptes Rendus. Math\'ematique},
pages = {711--716},
publisher = {Elsevier},
volume = {343},
number = {11-12},
year = {2006},
doi = {10.1016/j.crma.2006.09.036},
language = {en},
}
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] 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] The speed of propagation for KPP type problems. I – Periodic framework, J. Eur. Math. Soc., Volume 7 (2005), pp. 173-213
[7] Existence of non-planar solutions of a simple model of premixed Bunsen flames, SIAM J. Math. Anal., Volume 31 (1999), pp. 80-118
[8] Mathematical Aspects of Reacting and Diffusing Systems, Springer-Verlag, 1979
[9] Existence and qualitative properties of conical bistable fronts, Disc. Cont. Dyn. Systems, Volume 13 (2005), pp. 1069-1096
[10] Travelling waves and entire solutions of the Fisher-KPP equation in
[11] 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] Existence and global stability of traveling curved fronts in the Allen–Cahn equations, J. Differential Equations, Volume 213 (2005), pp. 204-233
[14] Biological Invasions: Theory and Practice, Oxford University Press, Oxford, 1997
[15] Existence of planar flame fronts in convective-diffusive periodic media, Arch. Ration. Mech. Anal., Volume 121 (1992), pp. 205-233
- A non-local bistable reaction-diffusion equation with a gap, Discrete Continuous Dynamical Systems - A, Volume 37 (2017) no. 2, p. 685 | DOI:10.3934/dcds.2017029
- Challenges in modeling biological invasions and population distributions in a changing climate, Ecological Complexity, Volume 20 (2014), p. 258 | DOI:10.1016/j.ecocom.2014.05.007
- Traveling fronts guided by the environment for reaction-diffusion equations, Networks Heterogeneous Media, Volume 8 (2013) no. 1, p. 79 | DOI:10.3934/nhm.2013.8.79
- Generalized fronts in reaction-diffusion equations with bistable nonlinearity, Acta Mathematica Sinica, English Series, Volume 28 (2012) no. 8, p. 1633 | DOI:10.1007/s10114-012-0015-5
- Generalized fronts in reaction–diffusion equations with mono-stable nonlinearity, Nonlinear Analysis: Theory, Methods Applications, Volume 74 (2011) no. 2, p. 433 | DOI:10.1016/j.na.2010.08.055
- Traveling waves in a one-dimensional heterogeneous medium, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 26 (2009) no. 3, p. 1021 | DOI:10.1016/j.anihpc.2009.02.003
- Bistable traveling waves around an obstacle, Communications on Pure and Applied Mathematics, Volume 62 (2009) no. 6, p. 729 | DOI:10.1002/cpa.20275
- Patch-size and isolation effects in the Fisher–Kolmogorov equation, Journal of Mathematical Biology, Volume 57 (2008) no. 4, p. 521 | DOI:10.1007/s00285-008-0174-2
- A population facing climate change: joint influences of Allee effects and environmental boundary geometry, Population Ecology, Volume 50 (2008) no. 2, p. 215 | DOI:10.1007/s10144-007-0073-1
Cité par 9 documents. Sources : Crossref
Commentaires - Politique
Vous devez vous connecter pour continuer.
S'authentifier