Nonlinear diffusion equations with nonlinear gradient noise

Konstantinos Dareiotis, Benjamin Gess

Published 2018-11-20, updated 2019-04-01Version 2

We prove the existence and uniqueness of entropy solutions for nonlinear diffusion equations with nonlinear conservative gradient noise. As particular applications our results include stochastic porous media equations, as well as the one-dimensional stochastic mean curvature flow in graph form.