Finite time extinction for stochastic sign fast diffusion and self-organized criticality

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, Da Prato, Röckner, CMP, 2009], [Barbu, Da Prato, Röckner, CRMAS, 2009], [Barbu, Röckner, CMP, 2012], [Barbu, Da Prato, Röckner, JMAA, 2012], [Röckner, Wang, JMLS, 2013], [Barbu, MMAS, 2013]. 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.

37 pages; some references added

References in corpus (5)

• Stochastic variational inequalities and applications to the total variation flow perturbed by linear multiplicative noise
• Random attractors for stochastic porous media equations perturbed by space-time linear multiplicative noise
• Multi-valued, singular stochastic evolution inclusions
• Stochastic porous media equations and self-organized criticality: convergence to the critical state in all dimensions
• General Extinction Results for Stochastic Partial Differential Equations and Applications

Cited by in corpus (5)

• Strong Feller Property and Irreducibility for Non-Linear Monotone SPDEs
• Numerical approximation of singular-degenerate parabolic stochastic PDEs
• Well-posedness of SVI solutions to singular-degenerate stochastic porous media equations arising in self-organised criticality
• Ergodicity for singular-degenerate porous media equations
• Improved regularity for the stochastic fast diffusion equation