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

Michael Röckner; Francesco Russo

doi:10.1007/s00028-016-0372-0

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

Michael Röckner
, Francesco Russo

Bielefeld University
Université Paris-Saclay

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1049-1062
Number of pages	14
Journal	Journal of Evolution Equations
Volume	17
Issue number	3
DOIs	https://doi.org/10.1007/s00028-016-0372-0
Publication status	Published - 1 Sept 2017
Externally published	Yes

Keywords

Infinite volume
Multiplicative noise
Porous media type equation
Stochastic Fokker–Planck type equation
Stochastic partial differential equations

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10.1007/s00028-016-0372-0

Cite this

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title = "Uniqueness for a class of stochastic Fokker–Planck and porous media equations",

abstract = "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.",

keywords = "Infinite volume, Multiplicative noise, Porous media type equation, Stochastic Fokker–Planck type equation, Stochastic partial differential equations",

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AU - Röckner, Michael

AU - Russo, Francesco

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N2 - 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.

AB - 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.

KW - Infinite volume

KW - Multiplicative noise

KW - Porous media type equation

KW - Stochastic Fokker–Planck type equation

KW - Stochastic partial differential equations

UR - https://www.scopus.com/pages/publications/84996628767

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DO - 10.1007/s00028-016-0372-0

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EP - 1062

JO - Journal of Evolution Equations

JF - Journal of Evolution Equations

IS - 3

ER -

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

Abstract

Keywords

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