2025/05/17 by Emine Çelik, Celik, Emine, Luan Hoang +3 · 1 citation
Computer Science · Mathematics · #35B45 #35G31 #35M13 #35Q35 #76S05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2505.11987
openalex publication_date 2025/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.