Stochastic porous media equation with Robin boundary conditions, gravity-driven infiltration and multiplicative noise
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909207771480064 |
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| author | Ciotir, Ioana Goreac, Dan Li, Juan Tonnoir, Antoine |
| author_facet | Ciotir, Ioana Goreac, Dan Li, Juan Tonnoir, Antoine |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12572 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic porous media equation with Robin boundary conditions, gravity-driven infiltration and multiplicative noise Ciotir, Ioana Goreac, Dan Li, Juan Tonnoir, Antoine Analysis of PDEs Probability 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. |
| title | Stochastic porous media equation with Robin boundary conditions, gravity-driven infiltration and multiplicative noise |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2405.12572 |