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Stochastic Porous Media Equations and Self-Organized Criticality

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Abstract

The existence and uniqueness of nonnegative strong solutions for stochastic porous media equations with noncoercive monotone diffusivity function and Wiener forcing term is proven. The finite time extinction of solutions with high probability is also proven in 1-D. The results are relevant for self-organized criticality behavior of stochastic nonlinear diffusion equations with critical states.

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Authors and Affiliations

  1. Institute of Mathematics “Octav Mayer”, Romanian Academy, Iasi, 700506, Romania

    Viorel Barbu

  2. Scuola Normale Superiore di Pisa, Piazza dei Cavalieri, 7, 56126, Pisa, Italy

    Giuseppe Da Prato

  3. Faculty of Mathematics, University of Bielefeld, D-33501, Bielefeld, Germany

    Michael Röckner

  4. Department of Mathematics and Statistics, Purdue University, 150 N. University Street, West Latayette, IN, 47907-2067, USA

    Michael Röckner

Authors
  1. Viorel Barbu
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  2. Giuseppe Da Prato
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  3. Michael Röckner
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Corresponding author

Correspondence to Giuseppe Da Prato.

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Communicated by P. Constantin

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Barbu, V., Prato, G.D. & Röckner, M. Stochastic Porous Media Equations and Self-Organized Criticality. Commun. Math. Phys. 285, 901–923 (2009). https://doi.org/10.1007/s00220-008-0651-x

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  • DOI: https://doi.org/10.1007/s00220-008-0651-x

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