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Finite Time Extinction for Stochastic Sign Fast Diffusion and Self-Organized Criticality

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Abstract

We prove finite time extinction for stochastic sign fast diffusion equations driven by linear multiplicative space-time noise, corresponding to the Bak–Tang–Wiesenfeld model for self-organized criticality. This solves a problem posed and left open in several works: (Barbu, Methods Appl Sci 36:1726–1733, 2013; Röckner and Wang, J Lond Math Soc (2) 87:545–560, 2013; Barbu et al. J Math Anal Appl 389:147–164, 2012; Barbu and Röckner, Comm Math Phys 311:539–555, 2012; Barbu et al., Comm Math Phys 285:901–923, 2009, C R Math Acad Sci Paris 347(1–2):81–84, 2009). The highly singular-degenerate nature of the drift in interplay with the stochastic perturbation causes the need for new methods in the analysis of mass diffusion, and several new estimates and techniques are introduced.

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  1. Department of Mathematics, University of Chicago, Chicago, IL, 60637, USA

    Benjamin Gess

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  1. Benjamin Gess
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Communicated by H. Spohn

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Gess, B. Finite Time Extinction for Stochastic Sign Fast Diffusion and Self-Organized Criticality. Commun. Math. Phys. 335, 309–344 (2015). https://doi.org/10.1007/s00220-014-2225-4

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