Path-by-path well-posedness of nonlinear diffusion equations with multiplicative noise
- Authors: Benjamin Fehrman, Benjamin Gess
- Preprint year: 2018
- First public date: 2018-07-11
- arXiv: 1807.04230
- Status: Published
- Publication type: Journal article
- Publication year: 2021
- Journal: Journal de mathématiques pures et appliquées, 148 (2021), pp. 221-266
- DOI: 10.1016/j.matpur.2021.01.004
Abstract
We prove the path-by-path well-posedness of stochastic porous media and fast diffusion equations driven by linear, multiplicative noise. As a consequence, we obtain the existence of a random dynamical system. This solves an open problem raised in [Barbu, Röckner; JDE, 2011], [Barbu, Röckner; JDE, 2018+], and [Gess, AoP, 2014].