Article Dans Une Revue Journal of Differential Equations Année : 2025

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

Résumé

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.

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hal-04580056 , version 1 (19-05-2024)

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Ioana Ciotir, Dan Goreac, Juan Li, Antoine Tonnoir. Stochastic porous media equation with Robin boundary conditions, gravity-driven infiltration and multiplicative noise. Journal of Differential Equations, 2025, 438, pp.113363. ⟨10.1016/j.jde.2025.113363⟩. ⟨hal-04580056⟩
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