Stochastic Porous Media Equations and Self-Organized Criticality

@article{Barbu2009StochasticPM,
  title={Stochastic Porous Media Equations and Self-Organized Criticality},
  author={Viorel Barbu and Giuseppe Da Prato and Michael R{\"o}ckner},
  journal={Communications in Mathematical Physics},
  year={2009},
  volume={285},
  pages={901-923}
}
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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