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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.

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Correspondence to Francesco Russo.

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Röckner, M., Russo, F. Uniqueness for a class of stochastic Fokker–Planck and porous media equations. J. Evol. Equ. 17, 1049–1062 (2017). https://doi.org/10.1007/s00028-016-0372-0

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  • DOI: https://doi.org/10.1007/s00028-016-0372-0

Mathematics Subject Classification

  • 35R60
  • 60H15
  • 82C31

Keywords

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