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. 
View PDF on arXiv
2 Citations
Background Citations
2
Methods Citations
1

2 Citations

Ergodicity for Singular-Degenerate Stochastic Porous Media Equations
  • Marius Neuß
  • 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…
Stochastic partial differential equations arising in self-organized criticality
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.

References

SHOWING 1-10 OF 67 REFERENCES
Stochastic Porous Media Equations and Self-Organized Criticality
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…
Ergodicity for singular-degenerate porous media equations.
The long time behaviour of solutions to generalised stochastic porous media equations on bounded domains with Dirichlet boundary data is studied. We focus on a degenerate form of nonlinearity arising…
Stochastic generalized porous media and fast diffusion equations
Entropy solutions for stochastic porous media equations
Existence of strong solutions for stochastic porous media equation under general monotonicity conditions
This paper addresses existence and uniqueness of strong solutions to stochastic porous media equations dX ( X)dt = B(X)dW (t) in bounded domains of R d with Dirichlet boundary conditions. Here is a…
Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE
We study quasilinear degenerate parabolic-hyperbolic stochastic partial differential equations with general multiplicative noise within the framework of kinetic solutions. Our results are twofold:…
Strong Solutions for Stochastic Partial Differential Equations of Gradient Type
Singular-Degenerate Multivalued Stochastic Fast Diffusion Equations
TLDR
A well-posedness framework based on Stochastic variational inequalities (SVI) is developed, characterizing solutions to the stochastic sign fast diffusion equation, previously obtained in a limiting sense only.
Existence and uniqueness of nonnegative solutions to the stochastic porous media equation
It is proved that the stochastic porous media equation in a bounded domain of R 3 , with multiplicative noise, with a monotone nonlin- earity of polynomial growth has a unique nonnegative solution in…
Ergodicity for Stochastic Porous Media Equations
The long time behaviour of solutions to stochastic porous media equations on smooth bounded domains with Dirichlet boundary data is studied. Based on weighted $L^{1}$-estimates the existence and…
...
...