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| We consider generalized Forchheimer (non-Darcy) flows of slightly compressible fluids in porous media. The resulting degenerate parabolic equation for pressure is studied in a bounded domain with time-dependent boundary data. We obtain long-time estimates for the $L^\infty$-norm of the pressure, its gradient and time derivative. Exploiting the special structure of the equation, we combine the De Giorgi and Ladyzhenskaya-Uraltseva iteration techniques with uniform Gronwall-type inequalities. This is joint work with Thinh Kieu and Tuoc Phan. |
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