Well-posedness of SVI solutions to singular-degenerate stochastic porous media equations arising in self-organized criticality

@article{Neu2020WellposednessOS,
  title={Well-posedness of SVI solutions to singular-degenerate stochastic porous media equations arising in self-organized criticality},
  author={Marius Neu{\ss}},
  journal={Stochastics and Dynamics},
  year={2020}
}
  • Marius Neuß
  • Published 4 February 2020
  • Mathematics
  • Stochastics and Dynamics
We consider a class of generalized stochastic porous media equations with multiplicative Lipschitz continuous noise. These equations can be related to physical models exhibiting self-organized criticality. We show that these SPDEs have unique SVI solutions which depend continuously on the initial value. In order to formulate this notion of solution and to prove uniqueness in the case of a slowly growing nonlinearity, the arising energy functional is analyzed in detail. 
Ergodicity for Singular-Degenerate Stochastic Porous Media Equations
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  • Mathematics
    Journal of Dynamics and Differential Equations
  • 2021
The long time behaviour of solutions to generalized stochastic porous media equations on bounded intervals with zero Dirichlet boundary conditions is studied. We focus on a degenerate form of
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TLDR
It is shown that the weakly driven Zhang model converges to a stochastic PDE with singular-degenerate diffusion and the deterministic BTW model is proved to converge to a singular- Degenerate PDE.

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