Path-by-path well-posedness of nonlinear diffusion equations with multiplicative noise
Probability
2020-05-05 v2 Analysis of PDEs
Dynamical Systems
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, R\"ockner; JDE, 2011], [Barbu, R\"ockner; JDE, 2018+], and [Gess, AoP, 2014].
Keywords
Cite
@article{arxiv.1807.04230,
title = {Path-by-path well-posedness of nonlinear diffusion equations with multiplicative noise},
author = {Benjamin Fehrman and Benjamin Gess},
journal= {arXiv preprint arXiv:1807.04230},
year = {2020}
}
Comments
37 pages