A fluid-solid interaction problem in porous media
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912897285750784 |
|---|---|
| author | Alonso-Orán, Diego Granero-Belinchón, Rafael |
| author_facet | Alonso-Orán, Diego Granero-Belinchón, Rafael |
| contents | In this work, we derive asymptotic interface models for an elastic Muskat free boundary problem describing Darcy flow beneath an elastic membrane. In a weakly nonlinear regime of small interface steepness, we obtain nonlocal evolution equations that capture the free-boundary dynamics up to quadratic order. In the long-wave thin-film regime, we rewrite the kinematic condition in flux form, flatten the moving domain, and derive a lubrication-type equation. Moreover, we establish well-posedness for these models in suitable Wiener spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10822 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A fluid-solid interaction problem in porous media Alonso-Orán, Diego Granero-Belinchón, Rafael Analysis of PDEs Fluid Dynamics In this work, we derive asymptotic interface models for an elastic Muskat free boundary problem describing Darcy flow beneath an elastic membrane. In a weakly nonlinear regime of small interface steepness, we obtain nonlocal evolution equations that capture the free-boundary dynamics up to quadratic order. In the long-wave thin-film regime, we rewrite the kinematic condition in flux form, flatten the moving domain, and derive a lubrication-type equation. Moreover, we establish well-posedness for these models in suitable Wiener spaces. |
| title | A fluid-solid interaction problem in porous media |
| topic | Analysis of PDEs Fluid Dynamics |
| url | https://arxiv.org/abs/2602.10822 |