A priori estimates for gaseous flows of Forchheimer-type in heterogeneous porous media

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Hauptverfasser: Celik, Emine, Hoang, Luan, Kieu, Thinh
Format: Preprint
Veröffentlicht: 2025
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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