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Archive for Rational Mechanics and Analysis

, Volume 233, Issue 1, pp 249–322 | Cite as

Well-Posedness of Nonlinear Diffusion Equations with Nonlinear, Conservative Noise

  • Benjamin Fehrman
  • Benjamin GessEmail author
Open Access
Article

Abstract

We prove the pathwise well-posedness of stochastic porous media and fast diffusion equations driven by nonlinear, conservative noise. As a consequence, the generation of a random dynamical system is obtained. This extends results of the second author and Souganidis, who considered analogous spatially homogeneous and first-order equations, and earlier works of Lions, Perthame, and Souganidis.

Notes

Acknowledgements

Open access funding provided by Max Planck Society. We would like to thank the referees for their careful reports. Their comments were of substantial benefit to the paper. The first author was supported by the National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship under Grant No. 1502731. The second author acknowledges financial support by the the Max Planck Society through the Max Planck Research Group “Stochastic partial differential equations” and by the DFG through the CRC “Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications”.

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Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK
  2. 2.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  3. 3.Fakultät für MathematikUniversität BielefeldBielefeldGermany

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