Well-posedness of the obstacle problem for stochastic nonlinear diffusion equations: an entropy formulation
Probability
2025-04-17 v2 Analysis of PDEs
Abstract
In this paper, we establish the existence, uniqueness and stability results for the obstacle problem associated with a degenerate nonlinear diffusion equation perturbed by conservative gradient noise. Our approach revolves round introducing a new entropy formulation for stochastic variational inequalities. As a consequence, we obtain a novel well-posedness result for the obstacle problem of deterministic porous medium equations with nonlinear reaction terms.
Cite
@article{arxiv.2404.02547,
title = {Well-posedness of the obstacle problem for stochastic nonlinear diffusion equations: an entropy formulation},
author = {Kai Du and Ruoyang Liu},
journal= {arXiv preprint arXiv:2404.02547},
year = {2025}
}
Comments
37 pages