Travelling waves and homogeneous fragmentation

Abstract : We formulate the notion of the classical Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) reaction diffusion equation associated with a homogeneous conservative fragmentation process and study its travelling waves. Specifically we establish existence, uniqueness and asymptotics. In the spirit of classical works such as McKean [31, 32], Neveu [34] and Chauvin [12] our analysis exposes the relation between travelling waves certain additive and multiplicative martingales via laws of large numbers which have been previously studied in the context of Crump- Mode-Jagers (CMJ) processes by Nerman [33] and in the context of fragmentation processes by Bertoin and Martinez [9] and Harris et al. [17]. The conclusions and methodology presented here appeal to a number of concepts coming from the theory of branching random walks and branching Brownian motion showing their mathematical robustness even within the context of fragmentation theory.
Type de document :
Pré-publication, Document de travail
2009
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https://hal.archives-ouvertes.fr/hal-00440215
Contributeur : Julien Berestycki <>
Soumis le : mercredi 9 décembre 2009 - 17:44:48
Dernière modification le : mercredi 12 octobre 2016 - 01:02:47

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  • HAL Id : hal-00440215, version 1
  • ARXIV : 0911.5179

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INSMI | PMA | UPMC | USPC

Citation

J. Berestycki, S. C. Harris, A. E. Kyprianou. Travelling waves and homogeneous fragmentation. 2009. 〈hal-00440215〉

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