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.
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Preprints, Working Papers, ...
2009
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https://hal.archives-ouvertes.fr/hal-00440215
Contributor : Julien Berestycki <>
Submitted on : Wednesday, December 9, 2009 - 5:44:48 PM
Last modification on : Wednesday, October 12, 2016 - 1:02:47 AM

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

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Citation

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

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