The obstacle problem for stochastic porous media equations

TL;DR

This paper establishes the existence and uniqueness of non-negative entropy solutions for the obstacle problem in stochastic porous media equations by combining entropy formulation with penalization techniques.

Contribution

It introduces a novel approach that merges entropy solutions with penalization methods to handle the obstacle problem in stochastic porous media equations.

Findings

Proved existence of solutions

Proved uniqueness of solutions

Developed a combined entropy and penalization method

Abstract

We prove the existence and uniqueness of non-negative entropy solutions of the obstacle problem for stochastic porous media equations. The core of the method is to combine the entropy formulation with the penalization method.