Path-by-path well-posedness of nonlinear diffusion equations with multiplicative noise

Author: 

Fehrman, B
Gess, B

Publication Date: 

11 July 2018

Last Updated: 

2021-06-20T15:36:00.58+01:00

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].

Symplectic id: 

926179

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article