# Uniqueness for a class of stochastic Fokker–Planck and porous media equations

@article{Rckner2016UniquenessFA, title={Uniqueness for a class of stochastic Fokker–Planck and porous media equations}, author={Michael R{\"o}ckner and Francesco G. Russo}, journal={Journal of Evolution Equations}, year={2016}, volume={17}, pages={1049-1062} }

The purpose of the present note consists of first showing a uniqueness result for a stochastic Fokker–Planck equation under very general assumptions. In particular, the second-order coefficients may be just measurable and degenerate. We also provide a proof for uniqueness of a stochastic porous media equation in a fairly large space.

## 5 Citations

Probabilistic Representation for Solutions to Nonlinear Fokker-Planck Equations

- Mathematics, Computer ScienceSIAM J. Math. Anal.
- 2018

One obtains a probabilistic representation for the entropic generalized solutions to a nonlinear Fokker-Planck equation in $\mathbb R^d$ with multivalued nonlinear diffusion term as density…

Doubly probabilistic representation for the stochastic porous media type equation

- Mathematics
- 2016

The purpose of the present paper consists in proposing and discussing a doubly probabilistic representation for a stochastic porous media equation in the whole space R^1 perturbed by a multiplicative…

McKean Feynman-Kac probabilistic representations of non-linear partial differential equations

- Mathematics
- 2019

This paper presents a partial state of the art about the topic of representation of generalized Fokker-Planck Partial Differential Equations (PDEs) by solutions of McKean Feynman-Kac Equations…

D ec 2 01 9 McKean Feynman-Kac probabilistic representations of non-linear partial differential equations

- 2019

This paper presents a partial state of the art about the topic of representation of generalized FokkerPlanck Partial Differential Equations (PDEs) by solutions of McKean Feynman-Kac Equations (MFKEs)…

From nonlinear Fokker-Planck equations to solutions of distribution dependent SDE.

- Mathematics
- 2018

We construct weak solutions to a class of distribution dependent SDE, of type
$dX(t)=b\left( X(t), \displaystyle\frac{d\mathcal{L}_{X(t)}}{dx}(X(t))\right) dt+\sigma\left(…

## References

SHOWING 1-10 OF 17 REFERENCES

A stochastic Fokker-Planck equation and double probabilistic representation for the stochastic porous media type equation.

- Mathematics
- 2014

The purpose of the present paper consists in proposing and discussing a double probabilistic representation for a porous media equation in the whole space perturbed by a multiplicative colored noise.…

Stochastic generalized porous media and fast diffusion equations

- Mathematics
- 2006

Abstract We present a generalization of Krylov–Rozovskii's result on the existence and uniqueness of solutions to monotone stochastic differential equations. As an application, the stochastic…

Uniqueness for Fokker-Planck equations with measurable coefficients and applications to the fast diffusion equation

- Mathematics
- 2012

The object of this paper is the uniqueness for a $d$-dimensional Fokker-Planck type equation with inhomogeneous (possibly degenerated) measurable not necessarily bounded coefficients. We provide an…

Probabilistic representation for solutions of an irregular porous media type equation.

- Mathematics
- 2008

We consider a porous media type equation over all of ℝ d , d = 1, with monotone discontinuous coefficient with linear growth, and prove a probabilistic representation of its solution in terms of an…

Probabilistic representation for solutions of a porous media type equation with Neumann boundary condition: the case of the half-line

- Mathematics
- 2013

The purpose of this paper consists in proposing a generalized solution for a porous media type equation on a half-line with Neumann boundary condition and prove a probabilistic representation of this…

Non-monotone stochastic generalized porous media equations☆

- Mathematics
- 2008

Abstract By using the Nash inequality and a monotonicity approximation argument, existence and uniqueness of strong solutions are proved for a class of non-monotone stochastic generalized porous…

Stochastic Porous Media Equations

- Mathematics
- 2016

This survey is devoted to the presentation of a few recent results concerning the existence, longtime behaviour and localization of solutions to stochastic porous media equations with linearly…

Fokker-planck-kolmogorov Equations

- Mathematics
- 2015

* Stationary Fokker-Planck-Kolmogorov equations* Existence of solutions* Global properties of densities* Uniqueness problems* Associated semigroups* Parabolic Fokker-Planck-Kolmogorov equations*…

Stochastic Equations in Infinite Dimensions

- Mathematics
- 2008

Preface Introduction Part I. Foundations: 1. Random variables 2. Probability measures 3. Stochastic processes 4. Stochastic integral Part II. Existence and Uniqueness: 5. Linear equations with…

Uniqueness of Solutions of the Initial-Value Problem for u sub t - delta phi(u) = 0.

- Mathematics
- 1978

Abstract : Equations of the form u sub t - delta phi(u) = 0 arise in mathematical models of many physical situations. The uniqueness of solutions of the associated initial-value problem in R…