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

Michael Röckner and Francesco Russo
october, 2017
Publication type:
Paper in peer-reviewed journals
Journal:
Journal of Evolution Equations, vol. 17 (3), pp. 1049-1062
Publisher:
Springer-Verlag
arXiv:
images/icons/icon_arxiv.png 1609.00165
Keywords :
stochastic partial differential equations; infinite volume; porous media type equation; multiplicative noise; stochastic Fokker-Planck type equation.
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.
BibTeX:
@article{Roc-Rus-2017,
    author={Michael Röckner and Francesco Russo },
    title={Uniqueness for a class of stochastic Fokker-Planck and porous 
           media equations },
    doi={10.1007/s00028-016-0372-0 },
    journal={Journal of Evolution Equations },
    year={2017 },
    month={10},
    volume={17 (3) },
    pages={1049--1062},
}