Well-posedness of nonlinear diffusion equations with nonlinear, conservative noise
- Authors: Benjamin Fehrman, Benjamin Gess
- Preprint year: 2017
- First public date: 2017-12-15
- arXiv: 1712.05775
- Status: Published
- Publication type: Journal article
- Publication year: 2019
- Journal: Archive for rational mechanics and analysis, 233 (2019) 1, pp. 249-322
- DOI: 10.1007/s00205-019-01357-w
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.