Stochastic porous media equation with Robin boundary conditions, gravity-driven infiltration and multiplicative noise

TL;DR

This paper introduces a new stochastic porous media model incorporating gravity, Robin boundary conditions, and multiplicative noise, providing qualitative well-posedness results for infiltration in porous media.

Contribution

It develops a novel mathematical framework for modeling gravity-driven infiltration with stochastic effects and Robin boundary conditions, advancing the understanding of such complex systems.

Findings

Proved well-posedness of the stochastic model

Analyzed effects of gravity and boundary conditions

Established qualitative properties of solutions

Abstract

We aim at studying a novel mathematical model associated to a physical phenomenon of infiltration in an homogeneous porous medium. The particularities of our system are connected to the presence of a gravitational acceleration term proportional to the level of saturation, and of a Brownian multiplicative perturbation. Furthermore, the boundary conditions intervene in a Robin manner with the distinction of the behavior along the inflow and outflow respectively. We provide qualitative results of well-posedness, the investigation being conducted through a functional approach.