A priori estimates for gaseous flows of Forchheimer-type in heterogeneous porous media
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918023637499904 |
|---|---|
| author | Celik, Emine Hoang, Luan Kieu, Thinh |
| author_facet | Celik, Emine Hoang, Luan Kieu, Thinh |
| contents | We study isentropic fluid flows of gases of the Forchheimer-type in heterogeneous porous media. The governing equation is a doubly nonlinear parabolic equation with coefficients depending on the spatial variables. Its solutions are subject to a nonlinear Robin boundary condition. We establish the estimates of the solutions for short time in terms of the initial and boundary data. For the proof, the multi-weight versions of the Sobolev inequality, parabolic Sobolev inequality and trace theorem are derived. They are then used to implement the Moser iteration for suitable weighted norms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11987 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A priori estimates for gaseous flows of Forchheimer-type in heterogeneous porous media Celik, Emine Hoang, Luan Kieu, Thinh Analysis of PDEs Mathematical Physics 35Q35, 76S05, 35B45, 35G31, 35M13 We study isentropic fluid flows of gases of the Forchheimer-type in heterogeneous porous media. The governing equation is a doubly nonlinear parabolic equation with coefficients depending on the spatial variables. Its solutions are subject to a nonlinear Robin boundary condition. We establish the estimates of the solutions for short time in terms of the initial and boundary data. For the proof, the multi-weight versions of the Sobolev inequality, parabolic Sobolev inequality and trace theorem are derived. They are then used to implement the Moser iteration for suitable weighted norms. |
| title | A priori estimates for gaseous flows of Forchheimer-type in heterogeneous porous media |
| topic | Analysis of PDEs Mathematical Physics 35Q35, 76S05, 35B45, 35G31, 35M13 |
| url | https://arxiv.org/abs/2505.11987 |