Total variation flow perturbed by gradient linear multiplicative noise
Ionuţ Munteanu, Michael Röckner · Infinite Dimensional Analysis Quantum Probability and Related Topics · 2018
We consider stochastic nonlinear diffusion equations with a highly singular diffusivity term and multiplicative gradient-type noise. We study existence and uniqueness of non-negative variational solutions in terms of stochastic variational inequalities. We also show the positivity preserving property of the solutions and extinction in finite time with probability one. These kinds of equations arise, e.g., in the use for simulation of image restoring techniques or for modeling turbulence.