Stochastic Generalized Porous Media Equations with Reflection

TL;DR

This paper constructs a non-negative Markovian solution for stochastic generalized porous media equations with reflection, establishing regularity, comparison principles, and analyzing invariant measures and ergodicity.

Contribution

It introduces a novel approach to solving stochastic porous media equations with reflection, including regularity results and ergodic properties.

Findings

Constructed a non-negative Markovian solution.

Proved regularity properties and comparison theorem.

Analyzed invariant measures and ergodicity.

Abstract

A non-negative Markovian solution is constructed for a class of stochastic generalized porous media equations with reflection. To this end, some regularity properties and a comparison theorem are proved for stochastic generalized porous media equations, which are interesting by themselves. Invariant probability measures and ergodicity of the solution are also investigated.